A Posteriori Error Estimates for Lumped Mass Finite Element Method for Linear Parabolic Problems Using Elliptic Reconstruction

Abstract

We study residual-based a posteriori error estimates for both the spatially discrete and the fully discrete lumped mass finite element approximation for parabolic problems in a bounded convex polygonal domain in (2). In particular, the space discretization uses finite element spaces that are assumed to be nested one and the time discretization is based on the backward Euler approximation. The main key features used in the analysis are the reconstruction technique and energy argument combined with the stability of L-2 projection in H-1(). The a posteriori error estimates we derive are optimal order in both the -norms.