Supercloseness on graded meshes for Q 1 finite element approximation of a reaction–diffusion equation

DURÁN, R.G.; LOMBARDI, A.L.; PRIETO, M.I.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

ELSEVIER SCIENCE BV

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 ]but with a stronger restriction on the graduation parameter. As a consequence we obtain almost optimal error estimates in the L2-norm thus completing the error analysis given in Durán and Lombardi (2005) [8].