Artículo
Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
Fecha de publicación:
04/2012
Editorial:
Oxford University Press
Revista:
Ima Journal Of Numerical Analysis
ISSN:
0272-4979
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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.
Palabras clave:
CONVECTION-DIFFUSION
,
GRADED MESHES
,
SUPERCONVERGENCE
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Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos(SEDE CENTRAL)
Articulos de SEDE CENTRAL
Articulos de SEDE CENTRAL
Citación
Durán, Rodrigo Gonzalo; Lombardi, Ariel Luis; Prieto, Mariana Ines; Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes; Oxford University Press; Ima Journal Of Numerical Analysis; 32; 2; 4-2012; 511-533
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