Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces
In this paper we prove error estimates for a piecewise Q1 average interpolation on anisotropic rectangular elements, i.e., rectangles with sides of different orders, in two and three dimensions. Our error estimates are valid under the condition that neighboring elements have comparable size. This is...
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2005
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paper:paper_00255718_v74_n252_p1679_Duran2023-06-08T14:53:14Z Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces Duran, Ricardo Guillermo Lombardi, Ariel L. Anisotropic elements Weighted norms In this paper we prove error estimates for a piecewise Q1 average interpolation on anisotropic rectangular elements, i.e., rectangles with sides of different orders, in two and three dimensions. Our error estimates are valid under the condition that neighboring elements have comparable size. This is a very mild assumption that includes more general meshes than those allowed in previous papers. In particular, strong anisotropic meshes arising naturally in the approximation of problems with boundary layers fall under our hypotheses. Moreover, we generalize the error estimates allowing on the right-hand side some weighted Sobolev norms. This extension is of interest in singularly perturbed problems. Finally, we consider the approximation of functions vanishing on the boundary by finite element functions with the same property, a point that was not considered in previous papers on average interpolations for anisotropic elements. As an application we consider the approximation of a singularly perturbed reaction-diffusion equation and show that, as a consequence of our results, almost optimal order error estimates in the energy norm, valid uniformly in the perturbation parameter, can be obtained. © 2005 American Mathematical Society. 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. 2005 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v74_n252_p1679_Duran http://hdl.handle.net/20.500.12110/paper_00255718_v74_n252_p1679_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 elements Weighted norms |
| spellingShingle |
Anisotropic elements Weighted norms Duran, Ricardo Guillermo Lombardi, Ariel L. Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces |
| topic_facet |
Anisotropic elements Weighted norms |
| description |
In this paper we prove error estimates for a piecewise Q1 average interpolation on anisotropic rectangular elements, i.e., rectangles with sides of different orders, in two and three dimensions. Our error estimates are valid under the condition that neighboring elements have comparable size. This is a very mild assumption that includes more general meshes than those allowed in previous papers. In particular, strong anisotropic meshes arising naturally in the approximation of problems with boundary layers fall under our hypotheses. Moreover, we generalize the error estimates allowing on the right-hand side some weighted Sobolev norms. This extension is of interest in singularly perturbed problems. Finally, we consider the approximation of functions vanishing on the boundary by finite element functions with the same property, a point that was not considered in previous papers on average interpolations for anisotropic elements. As an application we consider the approximation of a singularly perturbed reaction-diffusion equation and show that, as a consequence of our results, almost optimal order error estimates in the energy norm, valid uniformly in the perturbation parameter, can be obtained. © 2005 American Mathematical Society. |
| author |
Duran, Ricardo Guillermo Lombardi, Ariel L. |
| author_facet |
Duran, Ricardo Guillermo Lombardi, Ariel L. |
| author_sort |
Duran, Ricardo Guillermo |
| title |
Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces |
| title_short |
Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces |
| title_full |
Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces |
| title_fullStr |
Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces |
| title_full_unstemmed |
Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces |
| title_sort |
error estimates on anisotropic q1 elements for functions in weighted sobolev spaces |
| publishDate |
2005 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v74_n252_p1679_Duran http://hdl.handle.net/20.500.12110/paper_00255718_v74_n252_p1679_Duran |
| work_keys_str_mv |
AT duranricardoguillermo errorestimatesonanisotropicq1elementsforfunctionsinweightedsobolevspaces AT lombardiariell errorestimatesonanisotropicq1elementsforfunctionsinweightedsobolevspaces |
| _version_ |
1768543501873577984 |