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...
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todo:paper_02724979_v32_n2_p511_Duran2023-10-03T15:15:16Z Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes Durán, R.G. Lombardi, A.L. Prieto, M.I. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Durán, R.G. Lombardi, A.L. Prieto, M.I. 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. |
| format |
JOUR |
| author |
Durán, R.G. Lombardi, A.L. Prieto, M.I. |
| author_facet |
Durán, R.G. Lombardi, A.L. Prieto, M.I. |
| author_sort |
Durán, R.G. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_02724979_v32_n2_p511_Duran |
| work_keys_str_mv |
AT duranrg superconvergenceforfiniteelementapproximationofaconvectiondiffusionequationusinggradedmeshes AT lombardial superconvergenceforfiniteelementapproximationofaconvectiondiffusionequationusinggradedmeshes AT prietomi superconvergenceforfiniteelementapproximationofaconvectiondiffusionequationusinggradedmeshes |
| _version_ |
1807314834948096000 |