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

RICARDO G. DURÁN; MARIANA I. PRIETO; ARIEL L. LOMBARDI

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2013 vol. 242 p. 232 - 247

0377-0427

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] almost optimal error estimates in the L2-norm thus completing the error analysis given in Durán and Lombardi (2005) [8].