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Abstract:

In this paper we analyse the approximation of a model convection-diffusion equation by standard bilinear finite elements using the graded meshes introduced in Durán & Lombardi (2006, Finite element approximation of convection-diffusion problems using graded meshes. Appl. Numer. Math., 56, 1314-1325). Our main goal is to prove superconvergence results of the type known for standard elliptic problems, namely, that the difference between the finite element solution and the Lagrange interpolation of the exact solution, in the ε-weighted H 1-norm, is of higher order than the error itself. The constant in our estimate depends only weakly on the singular perturbation parameter. As a consequence of the superconvergence result we obtain optimal order error estimates in the L 2-norm. Also we show how to obtain a higher order approximation by a local postprocessing of the computed solution. © The author 2011. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Registro:

Documento: Artículo
Título:Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
Autor:Durán, R.G.; Lombardi, A.L.; Prieto, M.I.
Filiación:Departamento de Matemática, Universidad de Buenos Aires and IMAS-CONICET, Ciudad Universitaria, (1428) Buenos Aires, Argentina
Instituto de Ciencias, Universidad Nacional de General Sarmiento, Departamento de Matemática, Juan María Gutierrez 1150, (1613) Los Polvorines, Provincia de Buenos Aires, Argentina
Departamento de Matemática, FCEyN, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
Palabras clave:Convection-diffusion; Graded meshes; Superconvergence
Año:2012
Volumen:32
Número:2
Página de inicio:511
Página de fin:533
DOI: http://dx.doi.org/10.1093/imanum/drr005
Título revista:IMA Journal of Numerical Analysis
Título revista abreviado:IMA J. Numer. Anal.
ISSN:02724979
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02724979_v32_n2_p511_Duran

Referencias:

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Citas:

---------- APA ----------
Durán, R.G., Lombardi, A.L. & Prieto, M.I. (2012) . Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes. IMA Journal of Numerical Analysis, 32(2), 511-533.
http://dx.doi.org/10.1093/imanum/drr005
---------- CHICAGO ----------
Durán, R.G., Lombardi, A.L., Prieto, M.I. "Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes" . IMA Journal of Numerical Analysis 32, no. 2 (2012) : 511-533.
http://dx.doi.org/10.1093/imanum/drr005
---------- MLA ----------
Durán, R.G., Lombardi, A.L., Prieto, M.I. "Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes" . IMA Journal of Numerical Analysis, vol. 32, no. 2, 2012, pp. 511-533.
http://dx.doi.org/10.1093/imanum/drr005
---------- VANCOUVER ----------
Durán, R.G., Lombardi, A.L., Prieto, M.I. Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes. IMA J. Numer. Anal. 2012;32(2):511-533.
http://dx.doi.org/10.1093/imanum/drr005