Supercloseness on graded meshes for Q1 finite element approximation of a reaction–diffusion equation

Abstract

In this paper we analyze the standard piece-wise bilinear finite element approximation of a model reaction–diffusion problem. We prove supercloseness results when appropriate graded meshes are used. The meshes are those introduced in Durán and Lombardi (2005) [8] but with a stronger restriction on the graduation parameter. As a consequence we obtain almost optimal error estimates in the L 2 -norm thus completing the error analysis given in Durán and Lombardi (2005).