Papers

• Convergence rates for AFEM with $H^{-1}$ data (with A. Cohen and R. DeVore)
pdf


• Optimal multilevel methods for graded bisection grids (with L. Chen and J. Xu)
pdf


• First variation of the general curvature-dependent surface energy (with G. Dogan)
pdf


• Quasi-optimal cardinality of AFEM driven by nonresidual estimators (with J.M. Cascon)
IMA J. Numer. Anal. (to appear).
pdf


• Dynamics of biomembranes: effect of the bulk fluid (with A. Bonito and M.S. Pauletti)
Math. Model. Nat. Phenom. (to appear).
pdf


• Galerkin and Runge-Kutta methods: unified formulation, a posteriori estimates and nodal superconvergence (with G. Akrivis and Ch. Makridakis)
Numer. Math. (to appear).
pdf


• Geometrically consistent mesh modification (with A. Bonito and M.S. Pauletti)
SIAM J. Numer. Anal. 48 (2010), 1877--1899.
pdf


• Preconditioning a class of fourth order problems by operator splitting (with E. Baensch and P. Morin)
Numer. Math. (to appear).
pdf


• A hydrid variational front-tracking level set mesh generator for problems exhibiting large deformations and topological changes (with S. Walker)
J. Comp. Phys. 229 (2010), 6243-6269.
pdf


• A posteriori error analysis for a class of integral equations and variational inequalities (with T. von Petersdorff and C-S. Zhang)
Numer. Math. 116 (2010), 519.
pdf


• Quasi-optimal convergence rate of an adaptive discontinuous Galerkin method (with A. Bonito)
SIAM J. Numer. Anal. 48 (2010), 734--771.
pdf


• AFEM for the Laplace-Beltrami operator on graphs: design and conditional contraction property (with K. Mekchay and P. Morin)
Math. Comp. 80 (2011), 625-648.
pdf


• Mixed finite element method for electrowetting on dielectric with contact line pinning (with A. Bonito and S. Walker)
Interfaces Free Boundaries. 12 (2010), 85-119.
pdf


• Parametric FEM for geometric biomembranes (with A. Bonito and M.S. Pauletti)
J. Comp. Phys 229 (2010), 3171--3188.
pdf


• Electrowetting with contact line pinning: computational modeling and comparison with experiments (with S. Walker and B. Shapiro)
Phys. Fluids 21 (2009), 102103.
pdf


• A finite element method for the dynamics of orientational ordering in fluid membranes (with S. Bartels and G. Dolzmann)
Model. Math. Anal. Numer. 44 (2010), 1--32.
pdf


• Optimal order a posteriori error estimates for a class of Runge-Kutta Galerkin methods (with G. Akrivis and Ch. Makridakis)
Numer. Math. (to appear).
pdf


• Towards self-organization of decaying surface corrugations: A numerical study (with A. Bonito, D. Margetis, and J. Quah)
Phys. Rev. E 79 (2009), 050601(R).
pdf


• A variational shape optimization approach to image segmentation with the Mumford-Shah functional (with G. Dogan and P. Morin)
SIAM J. Sci. Comp. 30 (2008), 3028--3049.
pdf


• Quasi-optimal convergence rate for an adaptive finite element method (with J.M. Cascon, Ch. Kreuzer, and K. Siebert)
SIAM J. Numer. Anal. 46 (2008), 2524--2550.
pdf


• A safeguarded weighted dual residual method (with A. Veeser and M. Verani)
IMA J. Numer. Anal. 29 (2009), 126--140.
pdf


• Design and Convergence of AFEM in H(div;Omega) (with J.M. Cascon and K. Siebert)
Math. Models Methods Appl. Sci. 17 (2007), 1849--1881.
pdf


• A posteriori error analysis for parabolic variational inequalities (K-S. Moon, T. von Petersdorff, and C-S. Zhang)
Math. Model. Numer. Anal. 41 (2007), 485--511.
pdf


• Discrete gradient flows for shape optimization and applications (G. Dogan, P. Morin, and M. Verani)
Computer Methods Appl. Mech. Engrg. 196 (2007), 3898--3914.
pdf


• Pointwise a posteriori error estimates for semilinear elliptic problems (with A. Veeser and M. Verani)
Numer. Math. 104 (2006), 515-538.
pdf


• The finite element Gauge-Uzawa method. Part II : the Boussinesq equations (with J-H. Pyo)
Math. Models Methods Appl. Sci. 16 (2006), 1599--1626..
pdf


• Nonlinear evolution governed by accretive operators in Banach spaces: error control and applications (with G. Savar\'e)
Abstract , pdf


• A posteriori error analysis for higher order dissipative methods for evolution problems (with Ch. Makridakis)
Abstract , pdf


• The Gauge-Uzawa finite element method. Part I: the Navier-Stokes equations (with J-H. Pyo)
Abstract , pdf


• A posteriori error estimates for the Crank-Nicolson method for parabolic equations (with G. Akrivis and Ch. Makridakis)
Abstract , pdf


• Convergence of adaptive FEM for general elliptic PDE (with Khamron Mekchay)
Abstract , pdf


• Estimates of the finite element Stokes projection in $W^1_\infty$ (with V. Girault and R. Scott)
C.R. Acad. Sci. Paris, Serie I (to appear).
Abstract , pdf


• Maximum-norm stability of the finite element Stokes projection (with V. Girault and R. Scott)
J. Math. Pures Appl. (to appear).
Abstract , pdf


• A finite element method for surface diffusion: the parametric case (with E. Baensch and P. Morin)
J. Comp. Phys. (to appear).
Abstract , pdf


• A posteriori error analysis for the mean curvature flow of graphs (with O. Lakkis)
SIAM J. Numer. Anal. (to appear).
Abstract , pdf


• A posteriori error control for the Allen-Cahn problem: circumventing Gronwall's inequality (with D. Kessler and A. Schmidt)
M$^2$AN Math. Model. Numer. Anal., 38 (2004), 129-142.
Abstract , pdf


• Error estimates for semi-discrete Gauge methods for the Navier-Stokes equations: First order schemes (with J.-H. Pyo)
Math. Comp. (to appear)
Abstract , pdf


• Fully localized a posteriori error estimators and barrier sets for contact problems (with K.G. Siebert and A. Veeser)
SIAM J. Numer. Anal. (to appear)
Abstract , pdf


• Surface diffusion of graphs: Variational formulation, error analysis and simulations (with E. Baensch and P. Morin)
SIAM J. Numer. Anal. (to appear).
Abstract , pdf


• Optimal relaxation parameter for the Uzawa method (with J.-H. Pyo)
Numer. Math. (to appear).
Abstract , pdf


• Elliptic reconstruction and a posteriori error estimates for parabolic problems (with Ch. Makridakis)
SIAM J. Numer. Anal., 41 (2003), 1585-1594.
Abstract , pdf


• Convergence of Adaptive Finite Element Methods (with P. Morin and K. Siebert)
SIAM Review, 44 (2002), 631--658.
Abstract , pdf


• Pointwise a posteriori error control for elliptic obstacle problems (with K. Siebert and A. Veeser)
Numer. Math. Online DOI 10.1007/s00211-002-0411-3, Dec. 2002.
Abstract , pdf


• Local a Posteriori Error Estimates and Adaptive Control of Pollution Effects (with X. Liao)
Numer. Methods PDE, 19 (2003), 421-442.
Abstract , pdf


• An adaptive Uzawa FEM for the Stokes problem: Convergence without the inf-sup condition (with E. Baensch and P. Morin)
SIAM J. Numer. Anal., 40 (2002), 1207--1229.
Abstract , pdf


• Local problems on stars: a posteriori error estimation, convergence, and performance (with P. Morin and K. Siebert)
Math. Comp., 72 (2003), 1067--1097.
Abstract , pdf


• Small data oscillation implies the saturation assumption (with W. Doerfler)
Numer. Math., 91 (2002), 1-12.
Abstract , pdf


• Positivity preserving finite element approximation (with L.B. Wahlbin)
Math. Comp., 71 (2001), 1405-1419.
Abstract , pdf


• Pointwise a posteriori error analysis for an adaptive penalty finite element method for the obstacle problem (with D. French and S. Larsson)
Comput. Methods Appl. Math., 1 (2001), 18-38.
Abstract , pdf


• Data oscillation and convergence of adaptive FEM (with P. Morin and K. Siebert)
SIAM J. Numer. Anal., 38, 2 (2000), 466-488.
Abstract , Postscript


• A posteriori error control and adaptivity for a phase relaxation model(with Z. Chen and A. Schmidt)
Model. Math. Anal. Numer., 34 (2000), 775-797.
Abstract , Postscript


• A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations (with G. Savare and C. Verdi)
Comm. Pure Appl. Math., 53 (2000), 525-589.
Abstract , Postscript


• A characteristic Galerkin method with adaptive error control for the continuous casting problem (with Z. Chen and A. Schmidt)
Comput. Methods Appl. Mech. Engrg., 189 (2000), 249-276.
Abstract , Postscript


• Residual type a posteriori error estimates for elliptic obstacle problems (with Z. Chen)
Numer. Math., 84 (2000), 527-548.
Abstract , Postscript


• A $P^1-P^1$ finite element method for a phase relaxation model. Part II: Adaptively refined meshes (with X. Jiang and C. Verdi)
SIAM J. Numer. Anal., 36 (1999), 974-999.
Abstract , Postscript


• Error control for nonlinear evolution equations (with G. Savare and C. Verdi)
C.R. Acad. Sci. Paris, Serie I, 326 (1998), 1437-1442.
Abstract , Postscript


• A posteriori error estimation and adaptivity for degenerate parabolic problems (with A. Schmidt and C. Verdi)
Math. Comp., 69 (2000), 1-24.
Abstract , Postscript


• Adapting meshes and time-steps for phase change problems (with A. Schmidt and C. Verdi)
Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. Ia (9), 8 (1997), 273-292.
Abstract , Postscript (*.ps.gz) , pdf


• A $P^1-P^1$ finite element method for a phase relaxation model. Part I: Quasi-uniform mesh (with X. Jiang)
SIAM J. Numer. Anal., 35 (1998), 1176-1190.
Abstract , Postscript


• Combined effect of explicit time stepping and quadrature for curvature driven flows (with C. Verdi)
Numer. Math., 74 (1996), 105-136.
Abstract , Postscript


• Optimal error estimates for semidiscrete phase relaxation models (with X. Jiang)
RAIRO Model. Math. Anal. Numer., 31 (1997), 91-120.
Abstract , Postscript


• A dynamic mesh algorithm for curvature dependent evolving interfaces (with M. Paolini and C. Verdi)
J. Comp. Physics, 123 (1996), 296-310.
Abstract , Postscript


• Convergence past singularities for a fully discrete approximation of curvature driven interfaces (with C. Verdi)
SIAM J. Numer. Anal., 34 (1997), 490-512.
Abstract , Postscript


• A $P^1-P^0$ finite element method for a model of polymer crystallization (with X. Jiang and C. Verdi)
Comput. Methods Appl. Mech. Engrg., 125 (1995), 303-317.
Abstract , Postscript


• Convergence of double obstacle problems to the generalized geometric motion of fronts (with C. Verdi)
SIAM J. Math. Anal., 26 (1995), 1514-1526.
Abstract , Postscript


• Pointwise a posteriori error estimates for elliptic problems on highly graded meshes
Math. Comp., 64 (1995), 1-22.
Abstract , Postscript


• Quadratic rate of convergence for curvature dependent smooth interfaces: a simple proof (with M. Paolini and C. Verdi)
Appl. Math. Letters, 7 (1994), 59-63.
Abstract , Postscript


• Double obstacle formulation with variable relaxation parameter for smooth geometric front evolutions: asymptotic interface error estimates (with M. Paolini and C. Verdi)
Asymptotic Anal., 10 (1995), 173-198.
Abstract , Postscript


• Effect of numerical integration for elliptic obstacle problems (with X. Jiang)
Numer. Math., 67 (1994), 501-512.
Abstract , Postscript


• Removing the saturation assumption in a posteriori error analysis
Istit. Lombardo Accad. Sci. Lett. Rend. A, 127 (1993), 67-82.
Abstract , Postscript


• Sharp error analysis for curvature dependent evolving fronts (with M. Paolini and C. Verdi)
Math. Models Methods Appl. Sci. 3 (1993), 711-723
Abstract , Postscript


• Optimal interface error estimates for the mean curvature flow (with M. Paolini and C. Verdi)
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 21 (1994), 193-212
Abstract , Postscript