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Abstract:

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]. © 2012 Elsevier B.V. All rights reserved.

Registro:

Documento: Artículo
Título:Supercloseness on graded meshes for Q1 finite element approximation of a reaction-diffusion equation
Autor:Durán, R.G.; Lombardi, A.L.; Prieto, M.I.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
IMAS-CONICET, Intendente Güiraldes 2160, Ciudad Universitaria, Buenos Aires, Argentina
CONICET, Intendente Güiraldes 2160, Ciudad Universitaria, Buenos Aires, Argentina
Universidad Nacional de General Sarmiento, Juan María Gutierrez 1150, B1613GSX, Los Polvorines, Provincia de Buenos Aires, Argentina
Palabras clave:Finite elements; Graded meshes; Supercloseness; Superconvergence; Finite Element; Finite element approximations; Graded meshes; Optimal error estimate; Piece-wise; Reaction diffusion equations; Reaction diffusion problems; Super-convergence; Supercloseness; Finite element method; Linear equations; Mathematical models; Error analysis
Año:2013
Volumen:242
Número:1
Página de inicio:232
Página de fin:247
DOI: http://dx.doi.org/10.1016/j.cam.2012.10.004
Título revista:Journal of Computational and Applied Mathematics
Título revista abreviado:J. Comput. Appl. Math.
ISSN:03770427
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03770427_v242_n1_p232_Duran

Referencias:

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  • Linß, T., Stynes, M., Asymptotic analysis and shishkin-type decomposition for an elliptic convection-diffusion problem (2001) J. Math. Anal. Appl., 261, pp. 604-632
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Citas:

---------- APA ----------
Durán, R.G., Lombardi, A.L. & Prieto, M.I. (2013) . Supercloseness on graded meshes for Q1 finite element approximation of a reaction-diffusion equation. Journal of Computational and Applied Mathematics, 242(1), 232-247.
http://dx.doi.org/10.1016/j.cam.2012.10.004
---------- CHICAGO ----------
Durán, R.G., Lombardi, A.L., Prieto, M.I. "Supercloseness on graded meshes for Q1 finite element approximation of a reaction-diffusion equation" . Journal of Computational and Applied Mathematics 242, no. 1 (2013) : 232-247.
http://dx.doi.org/10.1016/j.cam.2012.10.004
---------- MLA ----------
Durán, R.G., Lombardi, A.L., Prieto, M.I. "Supercloseness on graded meshes for Q1 finite element approximation of a reaction-diffusion equation" . Journal of Computational and Applied Mathematics, vol. 242, no. 1, 2013, pp. 232-247.
http://dx.doi.org/10.1016/j.cam.2012.10.004
---------- VANCOUVER ----------
Durán, R.G., Lombardi, A.L., Prieto, M.I. Supercloseness on graded meshes for Q1 finite element approximation of a reaction-diffusion equation. J. Comput. Appl. Math. 2013;242(1):232-247.
http://dx.doi.org/10.1016/j.cam.2012.10.004