Error estimates for the Raviart-Thomas interpolation under the maximum angle condition
The classical error analysis for the Raviart-Thomas interpolation on triangular elements requires the so-called regularity of the elements, or equivalently, the minimum angle condition. However, in the lowest order case, optimal order error estimates have been obtained in [G. Acosta and R. G. Durán,...
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2008
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v46_n3_p1442_Duran http://hdl.handle.net/20.500.12110/paper_00361429_v46_n3_p1442_Duran |
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paper:paper_00361429_v46_n3_p1442_Duran2023-06-08T15:01:59Z Error estimates for the Raviart-Thomas interpolation under the maximum angle condition Duran, Ricardo Guillermo Lombardi, Ariel L. Anisotropic finite elements Mixed finite elements Raviart-Thomas Computational mechanics Error analysis Three dimensional Anisotropic finite elements Error estimates Lagrange interpolations Maximum angle conditions Mixed finite elements Raviart-Thomas Tetrahedral elements Triangular elements Interpolation The classical error analysis for the Raviart-Thomas interpolation on triangular elements requires the so-called regularity of the elements, or equivalently, the minimum angle condition. However, in the lowest order case, optimal order error estimates have been obtained in [G. Acosta and R. G. Durán, SIAM J. Nurner. Anal., 37 (2000), pp. 18-36] replacing the regularity hypothesis by the maximum angle condition, which was known to be sufficient to prove estimates for the standard Lagrange interpolation. In this paper we prove error estimates on triangular elements for the Raviart-Thomas interpolation of any order under the maximum angle condition. Also, we show how our arguments can be extended to the three-dimensional case to obtain error estimates for tetrahedral elements under the regular vertex property introduced in [G. Acosta and R. G. Durán, SIAM J. Numer. Anal., 37 (2000), pp. 18-36] © 2008 Society for Industrial and Applied Mathematics. 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. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v46_n3_p1442_Duran http://hdl.handle.net/20.500.12110/paper_00361429_v46_n3_p1442_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 |
Anisotropic finite elements Mixed finite elements Raviart-Thomas Computational mechanics Error analysis Three dimensional Anisotropic finite elements Error estimates Lagrange interpolations Maximum angle conditions Mixed finite elements Raviart-Thomas Tetrahedral elements Triangular elements Interpolation |
| spellingShingle |
Anisotropic finite elements Mixed finite elements Raviart-Thomas Computational mechanics Error analysis Three dimensional Anisotropic finite elements Error estimates Lagrange interpolations Maximum angle conditions Mixed finite elements Raviart-Thomas Tetrahedral elements Triangular elements Interpolation Duran, Ricardo Guillermo Lombardi, Ariel L. Error estimates for the Raviart-Thomas interpolation under the maximum angle condition |
| topic_facet |
Anisotropic finite elements Mixed finite elements Raviart-Thomas Computational mechanics Error analysis Three dimensional Anisotropic finite elements Error estimates Lagrange interpolations Maximum angle conditions Mixed finite elements Raviart-Thomas Tetrahedral elements Triangular elements Interpolation |
| description |
The classical error analysis for the Raviart-Thomas interpolation on triangular elements requires the so-called regularity of the elements, or equivalently, the minimum angle condition. However, in the lowest order case, optimal order error estimates have been obtained in [G. Acosta and R. G. Durán, SIAM J. Nurner. Anal., 37 (2000), pp. 18-36] replacing the regularity hypothesis by the maximum angle condition, which was known to be sufficient to prove estimates for the standard Lagrange interpolation. In this paper we prove error estimates on triangular elements for the Raviart-Thomas interpolation of any order under the maximum angle condition. Also, we show how our arguments can be extended to the three-dimensional case to obtain error estimates for tetrahedral elements under the regular vertex property introduced in [G. Acosta and R. G. Durán, SIAM J. Numer. Anal., 37 (2000), pp. 18-36] © 2008 Society for Industrial and Applied Mathematics. |
| author |
Duran, Ricardo Guillermo Lombardi, Ariel L. |
| author_facet |
Duran, Ricardo Guillermo Lombardi, Ariel L. |
| author_sort |
Duran, Ricardo Guillermo |
| title |
Error estimates for the Raviart-Thomas interpolation under the maximum angle condition |
| title_short |
Error estimates for the Raviart-Thomas interpolation under the maximum angle condition |
| title_full |
Error estimates for the Raviart-Thomas interpolation under the maximum angle condition |
| title_fullStr |
Error estimates for the Raviart-Thomas interpolation under the maximum angle condition |
| title_full_unstemmed |
Error estimates for the Raviart-Thomas interpolation under the maximum angle condition |
| title_sort |
error estimates for the raviart-thomas interpolation under the maximum angle condition |
| publishDate |
2008 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v46_n3_p1442_Duran http://hdl.handle.net/20.500.12110/paper_00361429_v46_n3_p1442_Duran |
| work_keys_str_mv |
AT duranricardoguillermo errorestimatesfortheraviartthomasinterpolationunderthemaximumanglecondition AT lombardiariell errorestimatesfortheraviartthomasinterpolationunderthemaximumanglecondition |
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1768544123486208000 |