A Posteriori Error Analysis for the Mean Curvature Flow of Graphs

Omar Lakkis
Institute of Applied and Computational Mathematics
FORTH PO Box 1527
GR-71110 Iraklio, Greece


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



We study the equation describing the motion of a nonparametric surface according to its mean curvature flow. This is a nonlinear nonuniformly parabolic PDE that can be discretized in space via a finite element method. We conduct an a posteriori error analysis of the spatial discretization and derive upper bounds of the error in terms of computable estimators based on local residual indicators. The reliability of the estimators is illustrated with two numerical simulations, one of which treats the case of a singular solution.