Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes

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, 13...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Duran, Ricardo Guillermo, Lombardi, Ariel L., Prieto, Mariana Inés
Publicado: 2012
Materias:
Convection-diffusion
Graded meshes
Superconvergence
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02724979_v32_n2_p511_Duran
http://hdl.handle.net/20.500.12110/paper_02724979_v32_n2_p511_Duran
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_02724979_v32_n2_p511_Duran
record_format dspace
spelling paper:paper_02724979_v32_n2_p511_Duran2023-06-08T15:25:18Z Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes Duran, Ricardo Guillermo Lombardi, Ariel L. Prieto, Mariana Inés Convection-diffusion Graded meshes Superconvergence 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. Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Lombardi, A.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Prieto, M.I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02724979_v32_n2_p511_Duran http://hdl.handle.net/20.500.12110/paper_02724979_v32_n2_p511_Duran
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Convection-diffusion
Graded meshes
Superconvergence
spellingShingle Convection-diffusion
Graded meshes
Superconvergence
Duran, Ricardo Guillermo
Lombardi, Ariel L.
Prieto, Mariana Inés
Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
topic_facet Convection-diffusion
Graded meshes
Superconvergence
description 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.
author Duran, Ricardo Guillermo
Lombardi, Ariel L.
Prieto, Mariana Inés
author_facet Duran, Ricardo Guillermo
Lombardi, Ariel L.
Prieto, Mariana Inés
author_sort Duran, Ricardo Guillermo
title Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
title_short Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
title_full Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
title_fullStr Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
title_full_unstemmed Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
title_sort superconvergence for finite element approximation of a convection-diffusion equation using graded meshes
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02724979_v32_n2_p511_Duran
http://hdl.handle.net/20.500.12110/paper_02724979_v32_n2_p511_Duran
work_keys_str_mv AT duranricardoguillermo superconvergenceforfiniteelementapproximationofaconvectiondiffusionequationusinggradedmeshes
AT lombardiariell superconvergenceforfiniteelementapproximationofaconvectiondiffusionequationusinggradedmeshes
AT prietomarianaines superconvergenceforfiniteelementapproximationofaconvectiondiffusionequationusinggradedmeshes
_version_ 1768542035145392128

Ejemplares similares