Eitan Tadmor: List of Publications (Subject Classification)

List of publications [by subject classification]
Other lists of publications: [by chronological order] [selected] [significant ] [ArXiv publications]

Reviews, Chapters in Books and Books Reviews, Chapters in Books and Books Stability of time-dependent schemes (linear) Runge-Kutta schemes Difference schemes and spectral methods for initial value problems Difference approximations for initial-boundary value problems Hyperbolic problems Hyperbolic systems with different time scales Convection diffusion problems Convection diffusion problems. Regularity and homogenization Incompressible Euler and related equations Critical threshold phenomena in Eulerian dynamics Collective dynamics Swarming, emergence and swarm-based optimization Nonlinear conservation laws and related equations Entropy functions and regularity Kinetic formulations and velcoity averaging Approximate methods for nonlinear PDEs Reviews and overviews Finite difference approximations. Total-variation and entropy stability Potential-based approximations of constraint transport equations Convergence rate estimates Non-oscillatory central schemes Nonlinear conservation laws Incompressible Euler, Navier-Stokes and related equations Hamilton-Jacobi equations Spectral methods Spectral recovery and detection of edges in spectral data Stability and convergence of spectral methods Spectral viscosity approximations Signal and image processing Multiscale representations in imaging and PDEs Matrix theory and computations The numerical radius, power-boundedness and eigen-solvers
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Reviews, Chapters in Books and Books
E. Tadmor Entropy stable schemes Handbook of Numerical Methods for Hyperbolic problems. Part A to appear. E. Tadmor A review of numerical methods for nonlinear partial differential equations Bull. AMS, 49(4) (2012) 507-554. E. Tadmor Selected topics in approximate solutions of nonlinear conservation laws. High-resolution central schemes ``Nonlinear Conservation Laws and Applications'' (A. Bressan, G-Q. Chen, M. Lewicka and D. Wang, eds), IMA Volumes in Mathematics and its Applications #153, Springer NY, (2011), pp. 101-122. B. Cheng & E. Tadmor Approximate periodic solutions for the rapidly rotating shallow-water and related equations ``Water Waves. Theory and Experiment'', Proceedings of the Conference held in Howard University, May 2008 (M. F. Mahmood, D. Henderson, H. Segur, eds), World Scientific (2010), pp. 69-78. E.Tadmor, J.-G. Liu & A. Tzavaras [AMS online catalogue] [Table of content ] Hyperbolic Problems: Theory, Numerics, Applications Proceedings of the Twelfth International Conference on Hyperbolic Problems held at the University of Maryland, College Park, June 9-13, 2008, AMS Proc. Symp. Appl. Math., 2009 Vol. 67.1: Plenary & Invited Talks, ISBN: 978-0-8218-4729-9 Vol. 67.2: Contributed Talks, ISBN: 978-0-8218-4730-5. E. Tadmor & W. Zhong Energy-preserving and stable approximations for the two-dimensional shallow water equations ``Mathematics and Computation - A Contemporary View", Proceedings of the third Abel Symposium held in Ålesund Norway May 2006 (H. Munthe-Kaas and B. Owren eds.), Abel Symposia 3, Springer (2008) 67-94. E. Tadmor Filters, mollifiers and the computation of the Gibbs phenomenon Acta Numerica v. 16 (2007) 305-378. E. Tadmor Entropy stability theory for difference approximations of nonlinear conservation laws and related time dependent problems Acta Numerica v. 12 (2003), 451-512. T. Hou & E. Tadmor [Springer online catalogue] [Table of content] Hyperbolic Problems: Theory, Numerics, Applications Proceedings of the Ninth International Conference on Hyperbolic Problems held in CalTech, Pasadena, March 25-29, 2002, Springer-Verlag (2003) ISBN: 3-540-44333-9. E. Tadmor High resolution methods for time dependent problems with piecewise smooth solutions "International Congress of Mathematicians", Proceedings of the ICM02 Beijing 2002 (Li Tatsien, ed.), Vol. III: Invited lectures, Higher Education Press, (2002) 747-757. E. Tadmor Approximate solution of nonlinear conservation laws and related equations ``Recent Advances in Partial Differential Equations and Applications" Proceedings of the 1996 Venice Conference in honor of Peter D. Lax and Louis Nirenberg on their 70th Birthday (R. Spigler and S. Venakides eds.), AMS Proceedings of Symposia in Applied Mathematics, 54 (1998) 325-368. E. Tadmor [html file] Approximate solutions of nonlinear conservation laws ``Advanced Numerical Approximation of Nonlinear Hyperbolic Equations" C.I.M.E. course in Cetraro, Italy, June 1997 (A. Quarteroni ed.), Lecture notes in Mathematics 1697, Springer Verlag (1998) 1-149. E. Tadmor Spectral methods for hyperbolic problems ``Methodes numeriques d'ordre eleve pour les ondes en regime transitoire", Lecture notes delivered at Ecole des Ondes, INRIA - Rocquencourt, January 24-28 (1994). E. Tadmor Super viscosity and spectral approximations of nonlinear conservation laws ``Numerical Methods for Fluid Dynamics IV", Proceedings of the 1992 Conference on Numerical Methods for Fluid Dynamics, (M. J. Baines and K. W. Morton, eds.), Clarendon Press, Oxford (1993) 69-82. E. Tadmor Stability analysis of finite-difference, pseudospectral and Fourier-Galerkin approximations for time-dependent problems SIAM Review 29 (1987), 525-555. D. Gottlieb & E. Tadmor [MR 90a:65041] Recovering pointwise values of discontinuous data within spectral accuracy ``Progress and Supercomputing in Computational Fluid Dynamics", Proceedings of a 1984 U.S.-Israel Workshop, Progress in Scientific Computing, Vol. 6 (E. M. Murman and S. S. Abarbanel, eds.), Birkhauser, Boston (1985), 357-375.
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Stability of Runge-Kutta schemes
E. Tadmor On the stability of Runge-Kutta methods for arbitrarily large systems of ODEs Communications on Pure & Applied Mathematics (2024). E. Tadmor From semi-discrete to fully discrete: stability of Runge-Kutta schemes by the energy method. II ``Collected Lectures on the Preservation of Stability under Discretization'', Lecture Notes from Colorado State University Conference, Fort Collins, CO, 2001 (D. Estep and S. Tavener, eds.) Proceedings in Applied Mathematics 109, SIAM 2002, 25-49. S. Gottlieb, C.-W. Shu & E. Tadmor Strong stability-preserving high order time discretization methods SIAM Review 43 (2001) 89-112. D. Levy & E. Tadmor From semi-discrete to fully-discrete: stability of Runge-Kutta schemes by the energy method SIAM Review 40 (1998) 40-73.
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Stability of difference and spectral approximations for initial value problems
E. Tadmor Spectral methods for hyperbolic problems "Methodes numeriques d'ordre eleve pour les ondes en regime transitoire", Lecture notes delivered at Ecole des Ondes, Inria - Rocquencourt January 24-28 (1994). E. Tadmor Stability analysis of finite-difference, pseudospectral and Fourier-Galerkin approximations for time-dependent problems SIAM Review 29 (1987), 525-555.
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Stability of difference approximations for initial-boundary value problems
M. Goldberg E. Tadmor Simple stability criteria for difference approximations of hyperbolic initial-boundary value problems ``Nonlinear Hyperbolic Equations - Theory, Computation Methods, and Applications", Proceedings of the 2^nd International Conference on Nonlinear Hyperbolic Problems, Notes on Numerical Fluid Mechanics, Vol. 24 (J. Ballmann and R. Jeltsch eds.), Vieweg Verlag (1988), 179-185. M. Goldberg & E. Tadmor Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems. II Mathematics of Computation 48 (1987), 503-520. M. Goldberg & E. Tadmor [MR 87b:65144] New stability criteria for difference approximations of hyperbolic initial-boundary value problems ``Large-Scale Computations in Fluid Mechanics", Proceedings of the 15^th AMS-SIAM Summer Seminar on Applied Mathematics held in Script Institute, San Diego, July 1983, Lectures in Applied Mathematics, Vol. 22-Part 1 (B. E. Engquist, S. Osher, and R. C. J. Somerville, eds.), American Mathematical Society, Rhode Island, (1985), 177-192. M. Goldberg & E. Tadmor Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems Mathematics of Computation 44 (1985), 361-377. E. Tadmor The unconditional instability of inflow-dependent boundary conditions in difference approximations to hyperbolic systems Mathematics of Computation 41 (1983), 309-319. E. Tadmor The unconditional instability of inflow-dependent boundary conditions in difference approximations to hyperbolic systems ``Numerical Boundary Condition Procedures", Proceedings of the 1981 NASA Ames Research Center Symposium on Numerical Boundary Condition Procedures (P. Kutler, ed.), NASA Ames (1982) 323-332. M. Goldberg & E. Tadmor Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. II Mathematics of Computation 36 (1981), 603-626. M. Goldberg & E. Tadmor Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. I Mathematics of Computation 32 (1978), 1097-1107.
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Hyperbolic problems. Systems with different time scales
E.Tadmor, J.-G. Liu & A. Tzavaras [AMS online catalogue] [Table of content] Hyperbolic Problems: Theory, Numerics, Applications Proceedings of the Twelfth International Conference on Hyperbolic Problems held at the University of Maryland, College Park, June 9-13, 2008, AMS Proc. Symp. Appl. Math. (2009) Vol. 67.1: Plenary & Invited Talks, ISBN: 978-0-8218-4729-9 Vol. 67.2: Contributed Talks, ISBN: 978-0-8218-4730-5. T. Hou & E. Tadmor [Springer online catalogue] [Table of content] Hyperbolic Problems: Theory, Numerics, Applications Proceedings of the Ninth International Conference on Hyperbolic Problems held in CalTech, Pasadena, March 25-29, 2002, Springer-Verlag (2003) ISBN: 3-540-44333-9. E. Tadmor Hyperbolic systems with different time scales Communications on Pure and Applied Mathematics 35 (1982), 839-866.
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Convection diffusion problems. Regularity and homogenization
S. He, E. Tadmor & A. Zlatoš On the fast spreading scenario Communications of the AMS 2 (2022) 149-171. S. He & E. Tadmor Multi-species Patlak-Keller-Segel system Indiana University Math Journal 70(4) (2021) 1577-1624. S. He & E. Tadmor Suppressing chemotactic blow-up through a fast splitting scenario on the plane Archive for Rational Mechanics and Analysis 232 (2019) 951-986. A. Biswas & E. Tadmor Dissipation versus quadratic nonlinearity: from a priori energy bound to higher-order regularizing effect Nonlinearity 27 (2014) 545-562. E. Tadmor Burgers' equation with vanishing hyper-viscosity Communications in Math. Sciences 2(2)(2004) 317-324. E. Tadmor & T. Tassa On the homogenization of oscillatory solutions to scalar convection-diffusion equations Advances in Mathematical Sciences and Applications 7(1) (1997), 93-117. E. Tadmor The well-posedness of the Kuramoto-Sivashinsky equation SIAM Journal on Mathematical Analysis 17 (1986), 884-893.
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Incompressible Euler, Navier-Stokes and related equations
H. Bae, A. Biswas & E. Tadmor Analyticity and decay estimates of the Navier-Stokes equations in critical Besov spaces Archive for Rational Mechanics and Analysis 205 (2012), 963-991. E. Tadmor On a new scale of regularity spaces with applications to Euler's equations Nonlinearity 14 (2001), 513-532. M. Lopes Filho, H. J. Nussenzveig & E. Tadmor Approximate solutions of the incompressible Euler equations with no concentrations Annales de l'institut Henri Poincare (c) Non Linear Analysis 17 (2000), 371-412.
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Critical threshold phenomena in Eulerian dynamics
Y.-P. Choi, D.-h. Kim, D. Koo & E. Tadmor Critical thresholds in pressureless Euler-Poisson equations with background states ArXiv:2402.12839 (2024). E. Tadmor & C. Tan Critical threshold for global regularity of Euler-Monge-Ampère system with radial symmetry SIAM Journal on Mathematical Analysis 54(4) (2022) 4277-4296 . D. Wei, E. Tadmor & H. Bae Critical thresholds in multi-dimensional Euler-Poisson equations with radial symmetry Communications in Mathematical Sciences 10(1) (2012), 75-86. H. Liu, E. Tadmor & D. Wei Global regularity of the 4D Restricted Euler Equations Physica D 239 (2010) 1225-1231. B. Cheng & E. Tadmor An improved local blow-up condition for Euler-Poisson equations with attractive forcing Physica D 238 (2009) 2062-2066. D. Chae & E. Tadmor On the finite time blow-up of the Euler-Poisson equations in Rⁿ Communications in Mathematical Sceinces 6(3) (2008) 785-789. B. Cheng & E. Tadmor Long time existence of smooth solutions for the rapidly rotating shallow-water and Euler equations SIAM Journal on Mathematical Analysis 39(5) (2008) 1668-1685. E. Tadmor & D. Wei On the global regularity of sub-critical Euler-Poisson equations with pressure Journal of the European Mathematical Society 10 (2008) 757-769. H. Liu & E. Tadmor Rotation prevents finite-time breakdown Physica D 188 (2004) 262-276. H. Liu & E. Tadmor Critical thresholds and conditional stability for Euler equations and related models ``Hyperbolic Problems: Theory, Numerics, Applications'', Proceedings of the 9th International Conference in Pasadena, Mar. 2002 (T. Hou and E. Tadmor, eds.), Springer (2003) 227-240. H. Liu & E. Tadmor Critical thresholds in 2D restricted Euler-Poisson equations SIAM Journal of Applied Mathematics63 (2003) 1889-1910. H. Liu & E. Tadmor Semi-classical limit of the nonlinear Schrödinger-Poisson equation with sub-critical initial data Methods and Applications in Analysis 9(4) (2002), 517-532. H. Liu & E. Tadmor Spectral dynamics of the velocity gradient field in restricted flows Communications in Mathematical Physics 228 (2002), 435-466. H. Liu & E. Tadmor Critical thresholds in a convolution model for nonlinear conservation laws SIAM Journal on Mathematical Analysis 33 (2001), 930-945. S. Engelberg, H. Liu & E. Tadmor Critical thresholds in Euler-Poisson equations Indiana University Math journal 50 (2001), 109-157..
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Nonlinear conservation laws. Entropy and regularity
A. Gouasmi, K. Duraisamy, S. M. Murman & E. Tadmor A minimum entropy principle in the compressible multicomponent Euler equations Mathematical Modelling and Numerical Analysis 54 (2020) 373-389. K. Karlsen, M. Rascle & E. Tadmor On the existence and compactness of a two-dimensional resonant system of conservation laws Communications in Mathematical Sciences 5(2) (2007) 253-265. E. Tadmor, M. Rascle & P. Bagnerini Compensated compactness for 2D conservation laws Journal of Hyperbolic Differential Equations 2(3) (2005) 697-712. E. Tadmor & T. Tassa On the piecewise regularity of entropy solutions to scalar conservation laws Communications on Partial Differential Equations 18 (1993), 1631-1652. E. Tadmor Entropy functions for symmetric systems of conservation laws Journal of Mathematical Analysis and Applications 122(2) (1987), 355-359. E. Tadmor A minimum entropy principle in the gas dynamics equations Applied Numerical Mathematics 2 (1986), 211-219.
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Collective dynamics: swarming, emergence and swarm-based optimization
J. Lu, E. Tadmor & A. Zenginoglu Swarm-based gradient descent method for non-convex optimization Communications of the AMS ArXiv:2211.17157 (2024). Z. Ding, M. Guerra, Q. Li & E. Tadmor Swarm-based gradient descent meets simulated annealing SIAM Journal on Numerical Analsysis ArXiv2404.18015 (2024). E. Tadmor & A. Zenginoglu Swarm-based optimization with random descent Acta Applicandae Mathematicae 190(2) (2024). J. Greene, E. Tadmor & M. Zhong (2023) The emergence of lines of hierarchy in collective motion of biological systems Physical Biology 20 (2023) 055001. E. Tadmor Swarming: hydrodynamic alignment with pressure Bulletin of AMS 60(3) (2023) 285-325. E. Tadmor Long time and large crowd dynamics of discrete Cucker-Smale alignment models Pure and Applied Functional Analysis 8(2) (2023) 603-626. J. Lu & E. Tadmor Hydrodynamic alignment with pressure II. Multispecies Quarterly of Applied Mathematics 81(2) (2023) 259-279. D. Lear, T. M. Leslie, R. Shvydkoy & E. Tadmor Geometric structure of mass concentration sets for pressureless Euler alignment systems Advances in Mathmematics 401(4) (2022) 108290. D. Hardin, E. Saff, R. Shu & E. Tadmor Dynamics of particles on a curve with pairwise hyper-singular repulsion Discrete & Continuous Dynamical Systems 41(12) (2021) 5509-5536. R. Shu & E. Tadmor Newtonian repulsion and radial confinement: convergence towards steady state Mathematical Models and Methods in Applied Sciences 31(7) (2021) 1297-1321. R. Shvydkoy & E. Tadmor Multi-flocks: emergent dynamics in systems with multi-scale collective behavior Multiscale Modeling and Simulation 19(2) (2021) 1115-1141. S. He & E. Tadmor A game of alignment: collective behavior of multi-species Annal. de l'institut Henri Poincare (c) Non Linear Analysis 38(4) (2021) 1031-1053. E. Tadmor On the mathematics of swarming: emergent behavior in alignment dynamics Notices of the AMS 68(4) (2021) 493-503. R. Shu & E. Tadmor Anticipation breeds alignment Archive for Rational Mechanics and Analysis 240 (2021) 203-241. R. Shvydkoy & E. Tadmor Topologically-based fractional diffusion and emergent dynamics with short-range interactions SIAM J. Math. Anal.52(6) (2020) 5792-5839. R. Shu & E. Tadmor Flocking hydrodynamics with external potentials Archive for Rational Mechanics and Analysis 238 (2020) 347-381.. J. Morales, J. Peszek & E. Tadmor Flocking with short-range interactions Journal of Statistical Physics 176 (2019) 382-397. R. Shvydkoy & E. Tadmor Eulerian dynamics with a commutator forcing III: Fractional diffusion of order 0<α<1 Physica D 376-377 (2018) 131-137. R. Shvydkoy & E. Tadmor Eulerian dynamics with a commutator forcing II: flocking Discrete and Continuous Dynamical Systems-A 37(11) (2017) 5503-5520. S. He & E. Tadmor Global regularity of two-dimensional flocking hydrodynamics Comptes rendus - Mathématique Ser. I 355 (2017) 795–805. R. Shvydkoy & E. Tadmor Eulerian dynamics with a commutator forcing (with erratum) Transactions of Mathematics and its Applications 1(1) (2017) 1-26. J. A. Carrillo, Y.-P. Choi E. Tadmor & C. Tan Critical thresholds in 1D Euler equations with nonlocal forces Mathematical Models and Methods in Applied Sciences 26(1) (2016) 185-206. E. Tadmor Mathematical aspects of self-organized dynamics: consensus, emergence of leaders, and social hydrodynamics SIAM News 48(9) 2015. C. Tan & E. Tadmor Critical thresholds in flocking hydrodynamics with nonlocal alignment Proceedings of the Royal Society A 372:20130401 (2014). S. Motsch & E. Tadmor Heterophilious dynamics enhances consensus SIAM Review 56(4) (2014) 577–621. S. Motsch & E. Tadmor A new model for self-organized dynamics and its flocking behavior Journal of Statistical Physics 144(5) (2011) 923-947. S.-Y. Ha & E. Tadmor From particle to kinetic and hydrodynamic descriptions of flocking Kinetic and Related Models 1(3) (2008) 415-435.
Kinetic formulations and velocity avergaing
P.-E Jabin, H.-Y. Lin & E. Tadmor Commutator method for averaging lemmas Analysis & PDE 15(6) (2022) 1561-1584 A new commutator method for averaging lemmas Séminaire Laurent Schwartz — EDP et applications (2019-2020), Talk no. 10 (2020). B. Gess, J. Sauer & E. Tadmor Optimal regularity in time and space for the porous medium equation Analysis & PDE 13(8) (2020) 2441-2480. E. Tadmor & T. Tao Velocity averaging, kinetic formulations and regularizing effects in quasilinear PDEs Communications on Pure & Applied Mathematics 60 (2007), 1488-1521. P.-L. Lions, P. Perthame & E. Tadmor Kinetic formulation of the isentropic gas dynamics and p-systems Communications in Mathematical Physics 163 (1994), 415-431. P.-L. Lions, P. Perthame & E. Tadmor A kinetic formulation of multidimensional scalar conservation laws and related equations Journal of the American Mathematical Society 7 (1994), 169-191. S. Schochet & E. Tadmor Regularized Chapman-Enskog expansion for scalar conservation laws Archive for Rational Mechanics and Analysis 119 (1992), 95-107. P.-L. Lions, B. Perthame & E. Tadmor [MR 91k:35156] Formulation cinétique des lois de conservation scalaires multidimensionelles Comptes Rendus de l'Académie des Sciences, Paris, Série I (1991), 97-102. B. Perthame & E. Tadmor A kinetic equation with kinetic entropy functions for scalar conservation Laws Communications in Mathematical Physics, 136 (1991), 501-517.
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Approximate methods for nonlinear PDEs. Reviews
E. Tadmor Entropy stability theory for difference approximations of nonlinear conservation laws and related time dependent problems Acta Numerica v. 12 (2003), 451-512. E. Tadmor High resolution methods for time dependent problems with piecewise smooth solutions ``International Congress of Mathematicians", Proceedings of the ICM02 Beijing 2002 (Li Tatsien, ed.), Vol. III: Invited lectures, Higher Education Press (2002) 747-757. E. Tadmor [html file] Approximate solutions of nonlinear conservation laws ``Advanced Numerical Approximation of Nonlinear Hyperbolic Equations", C.I.M.E. course in Cetraro, Italy, June 1997 (A. Quarteroni ed.), Lecture notes in Mathematics 1697, Springer Verlag (1998) 1-149. E. Tadmor Approximate solution of nonlinear conservation laws and related equations ``Recent Advances in Partial Differential Equations and Applications" Proceedings of the 1996 Venice Conference in honor of Peter D. Lax and Louis Nirenberg on their 70th Birthday (R. Spigler and S. Venakides eds.), AMS Proceedings of Symposia in Applied Mathematics 54 (1998) 325-368.
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Finite difference approximations. Total-variation and entropy stability
U. Fjordholm, R. Kappeli, S. Mishra & E. Tadmor Construction of approximate entropy measure valued solutions for hyperbolic systems of conservation laws Foundations of Computational Mathematics 17 (2017) 763–827. E. Tadmor Entropy stable schemes Handbook of Numerical Methods for Hyperbolic problems. Vol. XVII (R. Abgrall and C.-W. Shu, eds), Elsevier (2016) pp. 467-493. U. Fjordholm, S. Mishra & E. Tadmor On the computation of measure-valued solutions Acta Numerica 25 (2016) 567-679. E. Tadmor Perfect derivatives, conservative differences and entropy stable computation of hyperbolic conservation laws Discrete and Continuous Dynamical Systems-A 36(8) (2016) 4579-4598. U. Fjordholm, S. Mishra & E. Tadmor Entropy stable ENO scheme ``Hyperbolic Problems: Theory, Numerics, Applications'', Proceedings of the 13th International Conference held in Beijing, June 2010 (T. Li & S. Jiang, eds.), vol 1, Contemporary Appl. Math. 17, Higher Ed. Press (2012) 12-27. U. Fjordholm, S. Mishra & E. Tadmor ENO reconstruction and ENO interpolation are stable(+errata) Foundations of Computational Mathematics 13(2) (2012), 139-159. U. Fjordholm, S. Mishra & E. Tadmor Arbitrarily high order accurate entropy stable essentially non-oscillatory schemes for systems of conservation laws SIAM Jounral on Numerical Analysis 50(2), (2012) 544-573. U. Fjordholm, S. Mishra & E. Tadmor Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography Journal of Computational Physics 230 (2011), 5587-5609. M. Lukacova - Medvidova & E. Tadmor On the entropy stability of Roe-type finite volume methods ``Hyperbolic Problems: Theory, Numerics, Applications'', Proceedings of the 12th International Conference held in University of Maryland, June 2008 (E. Tadmor, J.-G. Liu & A. Tzavaras, eds.), AMS Proc. Symp. Applied Math., 67(2) (2009) 765-774. A. Madrane & E. Tadmor Entropy stability of Roe-type upwind finite volume methods on unstructured grids ``Hyperbolic Problems: Theory, Numerics, Applications'', Proceedings of the 12th International Conference held in University of Maryland, June 2008 (E. Tadmor, J.-G. Liu & A. Tzavaras, eds.), AMS Proc. Symp. Applied Math., 67(2) (2009) 775-784. U. Fjordholm, S. Mishra & E. Tadmor Energy preserving and energy stable schemes for the shallow water equations ``Foundations of Computational Mathematics", Proceedings of FoCM held in Hong Kong 2008 (F. Cucker, A. Pinkus & M. Todd, eds), London Math. Soc. Lecture Notes Ser. 363, (2009) 93-139. E. Tadmor & W. Zhong Energy-preserving and stable approximations for the two-dimensional shallow water equations ``Mathematics and Computation - A Contemporary View", Proceedings of the Third Abel Symposium held in Ålesund, Norway May 2006 (H. Munthe-Kaas & B. Owren eds.), Springer (2008) 67-94. E. Tadmor & W. Zhong Novel entropy stable schemes for 1D and 2D fluid equations ``Hyperbolic Problems: Theory, Numerics, Applications'', Proceedings of the 11^th International Conference in Lyon, July 2006 (S. Benzoni-Gavage and D. Serre, eds.), Springer (2007) 1111-1120. E. Tadmor & W. Zhong Entropy stable approximations of Navier-Stokes equations with no artificial numerical viscosity J. of Hyperbolic Differential Equations 3(3) (2006) 529-559. E. Tadmor On the entropy stability of difference schemes: a comparison principle and a homotopy approach ``Hyperbolic Problems: Theory, Numerics, Applications'', vol. I., Proceedings of the 10^th International Conference, Osaka, Sep. 2004 (F. Asukura, H. Aiso, S. Kawashima, A. Matsumura, S. Nishibata & K. Nishihara, eds.), Yokohama Publishers, (2006) 195-204. E. Tadmor Convenient total variation diminishing conditions for nonlinear difference schemes SIAM Journal on Numerical Analysis 25 (1988), 1002-1014. S. Osher & E. Tadmor On the convergence of difference approximations to scalar conservation laws Mathematics of Computation 50 (1988), 19-51. E. Tadmor The entropy dissipation by numerical viscosity in nonlinear conservative difference schemes ``Nonlinear Hyperbolic Problems'', Proceedings of a 1986 Advanced Research Workshop, Lecture Notes in Mathematics, Vol. 1270 (C. Carasso, P.-A. Raviart and D. Serre, eds.), Springer-Verlag, 1987, pp. 52-63. E. Tadmor The numerical viscosity of entropy stable schemes for systems of conservation laws. I. Mathematics of Computation 49 (1987), 91-103 [consult NASA Langley Report: "CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences" (references [87],[88])] E. Tadmor Entropy conservative finite element schemes ``Numerical Methods for Compressible Flows - Finite Difference Element and Volume Techniques", Proceedings of the winter annual meeting of the American Society of Mechanical Engineering (T. E. Tezduyar and T.J.R. Hughes, eds.), AMD-Vol. 78 (1986), 149-158. E. Tadmor Skew self-adjoint form for systems of conservation laws Journal of Mathematical Analysis and Applications 103(2) (1984) 428-442. E. Tadmor Numerical viscosity and the entropy condition for conservative difference schemes Mathematics of Computation 43 (1984), 369-381. E. Tadmor The large-time behavior of the scalar, genuinely nonlinear Lax-Friedrichs scheme Mathematics of Computation 43 (1984), 353-368.
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Potential-based approximations of constraint transport equations
S. Mishra & E. Tadmor Constraint preserving schemes using potential-based fluxes. III. Genuinely multi-dimensional schemes for the MHD equations Mathematical Modeling and Numerical Analysis 46 (2012) 661-680. S. Mishra & E. Tadmor Constraint preserving schemes using potential-based fluxes. II. Genuinely multi-dimensional systems of conservation laws SIAM Journal on Numerical Analysis 49(3) (2011) 1023-1045. S. Mishra & E. Tadmor Constraint preserving schemes using potential-based fluxes. I. Multidimensional transport equations Communications in Computational Physics 9(3) (2010) 688-710. S. Mishra & E. Tadmor Potential-based, constraint preserving, genuinely multi-dimensional schemes for systems of conservation laws ``Nonlinear Partial Differenetial Equations'', Proceedings of the 2008-2009 Special Year in Nonlinear PDEs held in Center Advanced Study, Oslo (H. Holden & K. Karlsen, eds.), AMS Contemporary Mathematics 526 (2010), 295-314. S. Mishra & E. Tadmor Vorticity preserving schemes using potential-based fluxes for the system wave equation ``Hyperbolic Problems: Theory, Numerics, Applications'', Proceedings of the 12th International Conference held in University of Maryland, June 2008 (E. Tadmor, J.-G. Liu & A. Tzavaras, eds.), AMS Proc. Symp. Applied Math., 67(2) (2009) 795-804
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Approximation of nonlinear conservation laws. Convergence rate estimates
E. Tadmor & T. Tang Pointwise error estimates for relaxation approximations to conservation laws SIAM Journal on Mathematical Analysis 32 (2001), 870-886. C.-T. Lin & E. Tadmor L¹-stability and error estimates for approximate Hamilton-Jacobi solutions Numerische Mathematik 87 (2001) 701-735. E. Tadmor & T. Tang Pointwise convergence rate for nonlinear conservation laws ``Hyperbolic Problems: Theory, Numerics, Applications'', Proceedings of the 7^th International Conference in Zurich, Feb. 1998 (M. Fey and R. Jeltsch, eds.), Int'l Series Numer. Math., Vol. 130, Birkhauser (1999) 925-934. E. Tadmor & T. Tang Pointwise error estimates for scalar conservation laws with piecewise smooth solutions SIAM Journal on Numerical Analysis 36 (1999) 1739-1756. A. Kurganov & E. Tadmor Stiff systems of hyperbolic conservation laws: convergence and error estimates SIAM Journal on Mathematical Analysis, 28 (1997) 1446-1456. H. Nessyahu, E. Tadmor & T. Tassa The convergence rate of Godunov type schemes SIAM Journal on Numerical Analysis, 31 (1994), 1-16. H. Nessyahu & E. Tadmor The convergence rate of approximate solutions for nonlinear scalar conservation laws SIAM Journal on Numerical Analysis, 29 (1992), 1505-1519. E. Tadmor Local error estimates for discontinuous solutions of nonlinear hyperbolic equations SIAM Journal on Numerical Analysis, 28 (1991), 891-906.
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Non-oscillatory central schemes. I. Nonlinear conservation laws
J. Lu & E. Tadmor Revisiting high-resolution schemes with van-Albada slope limiter Communications on Applied Mathematics and Computation 6 (2024) 1924–1953. O. Bhatoo, A. Peer, E. Tadmor, D. Tangman & A. Saib Conservative third-order central-upwind schemes for option pricing Pproblems Vietnam Journal of Mathematics 47 (2019) 813-833. O. Bhatoo, A. Peer, E. Tadmor, D. Tangman & A. Saib Efficient conservative second order central upwind schemes for option pricing problems Journal of Computational Finance, 22(5) (2019) 71-101. A. Chertock, S. Cui, A. Kurganov, S.-N. Özcan & E. Tadmor Well-balanced schemes for the Euler equations with gravitation: conservative formulation using global fluxes Journal of Computational Physics 358 (2018) 36–52. Y.-J. Liu, C.-W. Shu, E. Tadmor & M. Zhang Central local discontinuous Galerkin methods on overlapping cells for diffusion equations Mathematical Modeling and Numerical Analysis 45 (2011) 1009-1032. Y.-J. Liu, C.-W. Shu, E. Tadmor & M. Zhang L²-stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods Mathematical Modeling and Numerical Analysis 42 (2008) 593-607 [highlighted paper]. Y.-J. Liu, C.-W. Shu, E. Tadmor & M. Zhang Non-Oscillatory hierarchical reconstruction for central and finite volume schemes Communications in Computational Physics 2(5) (2007) 933-963. Y.-J. Liu, C.-W. Shu, E. Tadmor & M. Zhang Central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction SIAM Jounrnal on Numerical Analysis 45(6) (2007) 2442-2467. J. Balbas & E. Tadmor Non-oscillatory central schemes for one- and two-dimensional MHD equations. II: high-order semi-discrete schemes SIAM Journal on Scientific Computing 28 (2006) 533-560. J. Balbas & E. Tadmor A central differencing simulation of the Orszag-Tang vortex system IEEE Transactions on Plasma Science, The 4^th Triennial Special Issue on Images in Plasma Science 33(2) (2005) 470-471. J. Balbas, E. Tadmor, & C.-C. Wu [Numerical simulations] Non-oscillatory central schemes for one- and two-dimensional MHD equations Journal of Computational Physics 201 (2004) 261-285. A. Kurganov & E. Tadmor Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers Numerical Methods for Partial Differential Equations, 18 (2002) 548-608. A. Kurganov & E. Tadmor New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations Journal of Computational Physics, 160 (2000) 214-282. G.-S. Jiang, D. Levy, C.-T. Lin, S. Osher & E. Tadmor High-resolution non-oscillatory central schemes with non-staggered grids for hyperbolic conservation laws SIAM Journal on Numerical Analysis, 35 (1998) 2147-2168. D. Levy & E. Tadmor Non-oscillatory boundary treatment for staggered central schemes G.-S. Jiang & E. Tadmor Non-oscillatory central schemes for multidimensional hyperbolic conservation laws SIAM Journal on Scientific Computing 19 (1998), 1892-1917. X-D. Liu & E. Tadmor Third order nonoscillatory central scheme for hyperbolic conservation laws Numerische Mathematik 79 (1998), 397-425. H. Nessyahu & E. Tadmor Non-oscillatory central differencing for hyperbolic conservation laws Journal of Computational Physics 87 (1990), 408-463.
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Non-oscillatory central schemes. II. Incompressible Euler equations
D. Levy & E. Tadmor, reprint with embedded figures: , preprint with original figures: Non-oscillatory central schemes for the incompressible 2-D Euler equations Mathematical Research Letters, 4(3) (1997) 321-340. R. Kupferman & E. Tadmor A fast high-resolution second-order central scheme for incompressible flows Proceedings of the National Academy of Sciences 94 (1997) 4848-4852.
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Non-oscillatory central schemes. III. Hamilton-Jacobi equations
C.-T. Lin & E. Tadmor L¹-stability and error estimates for approximate Hamilton-Jacobi solutions Numerische Mathematik 87 (2001) 701-735. C.-T. Lin & E. Tadmor High-resolution non-oscillatory central scheme for Hamilton-Jacobi equations SIAM Journal on Scientific Computation 21 (2000) 2163-2186. A. Kurganov & E. Tadmor New high-resolution semi-discrete central schemes for Hamilton-Jacobi equations Journal of Computational Physics 160 (2000) 720-742.
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Spectral recovery and detection of edges in spectral data
E. Tadmor & J. Zou Novel edge detection methods for incomplete and noisy spectral data Journal of Fourier Analysis and Applications 14(5) (2008) 744-763. S. Engelberg & E. Tadmor Recovery of edges from spectral data with noise---a new perspective SIAM Journal on Numerical Analysis 46(5) (2008) 2620-2635. E. Tadmor Filters, mollifiers and the computation of the Gibbs phenomenon Acta Numerica 16 (2007) 305-378. A. Gelb & E. Tadmor Adaptive edge detectors for piecewise smooth data based on the minmod limiter Journal of Scientific Computing 28(2-3) (2006) 279-306. E. Tadmor & J. Tanner Adaptive filters for piecewise smooth spectral data IMA Journal of Numerical Analysis 25(4) (2005) 635-647. E. Tadmor & J. Tanner An adaptive order Godunov type central scheme "Hyperbolic Problems: Theory, Numerics, Applications", Proceedings of the 9th International Conference held in CalTech Pasadena, Mar. 2002 (T. Hou and E. Tadmor, eds.), Springer (2003) 871-880. A. Gelb & E. Tadmor Spectral reconstruction of one- and two-dimensional piecewise smooth functions from their discrete data Mathematical Modeling and Numerical Analysis 36 (2002) 155-175. E. Tadmor & J. Tanner Adaptive mollifiers -- high resolution recovery of piecewise smooth data from its spectral information Foundations of Computational Mathematics 2(2) (2002) 155-189. A. Gelb & E. Tadmor Detection of edges in spectral data II. Nonlinear enhancement SIAM Journal on Mumerical Analysis 38 (2000), 1389-1408. A. Gelb & E. Tadmor Detection of edges in spectral data Applied and Computational Harmonic Analysis 7 (1999) 101-135. S. Abarbanel, D. Gottlieb & E. Tadmor Spectral methods for discontinuous problems "Numerical Methods for Fluid Dynamics II", Proceedings of the 1985 Conference on Numerical Methods for Fluid Dynamics (K. W. Morton and M. J. Baines, eds.), Clarendon Press, Oxford (1986), 129-153. E. Tadmor The exponential accuracy of Fourier and Chebyshev differencing methods SIAM Journal on Numerical Analysis 23 (1986), 1-10. D. Gottlieb & E. Tadmor [SIAM Rev 28(4) 1986] [MR 90a:65041] Recovering pointwise values of discontinuous data within spectral accuracy &qout;Progress and Supercomputing in Computational Fluid Dynamics", Proceedings of a 1984 U.S.-Israel Workshop, Progress in Scientific Computing, Vol. 6 (E. M. Murman and S. S. Abarbanel, eds.), Birkhauser, Boston (1985) 357-375.
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Stability and convergence of spectral methods
C. Bardos & E. Tadmor Stability and spectral convergence of Fourier method for nonlinear problems. On the shortcomings of the 2/3 de-aliasing method Numerische Mathematik 129 (2014) 749-782. J. Goodman, T. Hou & E. Tadmor On the stability of the unsmoothed Fourier method for hyperbolic equations Numerische Mathematik 67(1) (1994), 93-129. D. Gottlieb & E. Tadmor The CFL condition for spectral approximations to hyperbolic initial-boundary value problems Mathematics of Computation 56 (1991), 565-588. E. Tadmor (1991) Essentially non-oscillatory spectral viscosity approximations "Hyperbolic Problems - Theory, Numerical Methods and Applications", Proceedings of the 3^rd International Conference on Hyperbolic Problems, Vol. II (B. Engquist and B. Gustafsson, eds.), Studentlitteratur and Chartwell-Bratt (1991), 861-873. D. Gottlieb, L. Lustman & E. Tadmor Convergence of spectral methods for hyperbolic initial-boundary value systems SIAM Journal on Numerical Analysis 24 (1987), 532-537. D. Gottlieb, L. Lustman & E. Tadmor Stability analysis of spectral methods for hyperbolic initial-boundary value systems SIAM Journal on Numerical Analysis 24 (1987), 241-256.
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Spectral viscosity approximations
E. Tadmor & K. Waagan Adaptive spectral viscosity for hyperbolic conservation laws SIAM journal on Scientific Computation 34(2) (2012), 993-1009. B.-Y. Guo, H.-P. Ma & E. Tadmor Spectral vanishing viscosity method for nonlinear conservation laws SIAM Journal on Numerical Analysis 39 (2001), 1254-1268. A. Gelb & E. Tadmor Enhanced spectral viscosity approximations for conservation laws Applied Numerical Mathematics 33 (2000), 3-21. G.-Q. Chen, Q. Du & E. Tadmor Spectral viscosity approximations to multidimensional scalar conservation laws Mathematics of Computation 61 (1993), 629-643. E. Tadmor Super viscosity and spectral approximations of nonlinear conservation laws "Numerical Methods for Fluid Dynamics IV", Proceedings of the 1992 Conference on Numerical Methods for Fluid Dynamics, (M. J. Baines and K. W. Morton, eds.), Clarendon Press, Oxford (1993) 69-82. E. Tadmor Total-variation and error estimates for spectral viscosity approximations Mathematics of Computation 60 (1993), 245-256. Y. Maday, S. M. Ould Kaber & E. Tadmor Legendre pseudospectral viscosity method for nonlinear conservation laws SIAM Journal on Numerical Analysis 30 (1993), 321-342. E. Tadmor [MR 92b:65076] Essentially non-oscillatory spectral viscosity approximations "Hyperbolic Problems - Theory, Numerical Methods and Applications", Proceedings of the 3rd International Conference on Hyperbolic Problems, Vol. II (B. Engquist and B. Gustafsson, eds.), Studentlitteratur and Chartwell-Bratt (1991) 861-873. E. Tadmor Shock capturing by the spectral viscosity method ``Spectral and High Order Methods for Partial Differential Equations", Proceedings of the ICOSAHOM '89 Conference held in Como, Italy 1989 (C. Canuto and A. Quarteroni, eds), North-Holannd (1990) 197-208; Computer Methods in Applied Mechanics and Engineering 78 (1990), 197-208. Y. Maday & E. Tadmor Analysis of the spectral vanishing viscosity method for periodic conservation laws SIAM Journal on Numerical analysis 26 (1989), 854-870. E. Tadmor Convergence of the spectral viscosity method for nonlinear conservation laws "11th International Conference on Numerical Methods in Fluid Dynamics", Lecture Notes in Physics, Vol. 323 (D. L. Dwoyer, M. Y. Hussaini, and R. G. Voigt, eds.), Springer-Verlag (1989) 548-552. E. Tadmor Convergence of spectral methods for nonlinear conservation laws SIAM Journal on Numerical Analysis 26 (1989), 30-44.
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Signal and image processing
S. Foucart, E. Tadmor & M. Zhong On the sparsity of LASSO minimizers in sparse data recovery Constructive Approximation 57 (2023) 901-919.
Multiscale representations in imaging and PDEs
A. Cohen, R. DeVore & E. Tadmor *Constructions of bounded solutions of div* u=f in critical spaces** in ``Multiscale, Nonlinear and Adaptive Approximation II'' (R. DeVore and A. Kunoth, eds), Springer, ISBN: 9783031758010, 2024 pp. 177-200. E. Tadmor Hierarchical construction of bounded solutions in critical regularity spaces Communications in Pure & Applied Mathematics 69(6) (2016) 1087-1109. E. Tadmor & C. Tan Hierarchical construction of bounded solutions of div U=F in critical regularity spaces "Nonlinear Partial Differential Equations", Proceedings of the 2010 Abel Symposium held in Oslo, Sep. 2010 (H. Holden & K. Karlsen eds.), Abel Symposia 7, Springer 2011, 255-269. P. Athavale & E. Tadmor Integro-differential equations based on (BV, L¹) image decomposition SIAM journal on Imaging Sciences 4(1) (2011) 300-312. P. Athavale & E. Tadmor Novel integro-differential equations in image processing and its applications "Computational Imaging VIII", Proceedings of SPIE meeting held Jan. 2010, San Jose (C. A. Bouman, I. Pollak, P. J. Wolfe eds.), vol. 7533, 75330S. E. Tadmor & P. Athavale Multiscale image representation using integro-differential equations Inverse Problems and Imaging 3(4) (2009) 693-710. E. Tadmor, S. Nezzar & L. Vese Multiscale hierarchical decomposition of images with applications to deblurring, denoising and segmentation Communications in Mathematical Sciences 6(2) (2008) 281-307. E. Tadmor, S. Nezzar & L. Vese A multiscale image representation using hierarchical (BV,L²) decompositions Multiscale Modeling and Simulations 2(4) (2004) 554-579.
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Matrix theory -- the numerical radius, power-boundedness and eigen-solvers
D. Gill & E. Tadmor An O(N²) method for computing the eigensystem of N x N symmetric tridiagonal matrices by the divide and conquer approach SIAM Journal on Scientific and Statistical Computing 11 (1990), 161-173. D. Gill & E. Tadmor An O(N²) method for computing the eigensystem of N x N symmetric tridiagonal matrices by the divide and conquer approach; Short communication Linear Algebra and its Applications 120, (1989), 257-258 . E. Tadmor The resolvent condition and uniform power-boundedness "Haifa Conference on Matrix Theory", Report (A. Berman, Y. Censor and H. Schneider, eds.) Linear Algebra and Its Applications 80 (1986), 250-252. E. Tadmor Complex symmetric matrices with strongly stable iterates Linear Algebra and Its Applications 78 (1986), 65-77. S. Friedland & E. Tadmor Optimality of the Lax-Wendroff condition Linear Algebra and its Applications 56 (1984), 121-129. M. Goldberg & E. Tadmor On the numerical radius and its applications Linear Algebra and its Applications 42 (1982), 263-284. E. Tadmor The equivalence of L²-stability, the resolvent condition and strict H-stability Linear Algebra and its Applications 41 (1981), 151-159. M. Goldberg, E. Tadmor & G. Zwas Numerical radius of positive matrices Linear Algebra and its Applications 12 (1975), 209-214. M. Goldberg, E. Tadmor & G. Zwas The numerical radius and spectral matrices Linear and Multilinear Algebra 2 (1975), 317-326. [Acknowledgement]