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

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

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 t...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 242; pp. 232 - 247
Main Authors: Durán, R.G., Lombardi, A.L., Prieto, M.I.
Format: Journal Article
Language:English
Published: Elsevier B.V 01-04-2013
Subjects:
Finite elements
Graded meshes
Supercloseness
Superconvergence
Finite elements
Graded meshes
Superconvergence
65N30
Supercloseness
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Summary: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].
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2012.10.004