Quadratic rate of convergence for curvature dependent smooth interfaces: a simple proof

Appl. Math. Letters, 7 (1994), 59-63.

Ricardo H. Nochetto
Department of Mathematics
University of Maryland, College Park
College Park, MD 20742, USA

rhn@math.umd.edu

Maurizio Paolini
Dipartimento di Matematica
Universita di Milano
Milano, 20133, Italy

paolini@galileo.dmf.bs.unicatt.it

Claudio Verdi
Dipartimento di Matematica
Universita di Milano
Milano, 20133, Italy

verdi@paola.mat.unimi.it

Abstract

We consider the approximation of curvature dependent geometric front evolutions by singularly perturbed parabolic double obstacle problems with small parameter $\eps$. We give a simplified proof of optimal interface error estimates of order $\O(\eps^2)$, valid in the smooth regime, which is based on constructing precise barriers, perturbing the forcing term and exploiting the maximum principle.