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

• Autores: Ricardo G. Durán, Ariel L. Lombardi, M. I. Prieto
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 242, Nº 1, 2013, págs. 232-247
• Idioma: inglés
• DOI: 10.1016/j.cam.2012.10.004
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• Resumen

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