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

DURÁN, RICARDO GUILLERMO; LOMBARDI, ARIEL LUIS; PRIETO, MARIANA INES

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

ELSEVIER SCIENCE BV

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

0377-0427

In this paper we analize the standard piece-wise bilinear finite element approximationof a model reaction-diffusion problem. We prove supercloseness results when appropriate gradedmeshes are used. The meshes are those introduced in [4] but with a stronger restriction on thegraduation parameter. As a consequence we obtain almost optimal error estimates in the L2-normthus completing the error analysis given in [4].[4] R. G. Durán and A. L. Lombardi, Error estimates on anisotropic Q1 elements for functionsin weighted sobolev spaces, Math. Comp., 74 (2005), pp. 1679:1706.