Interpolation error estimates for edge elements on anisotropic meshes
The classical error analysis for Nédélec edge interpolation requires the so-called regularity assumption on the elements. However, in Nicaise (2001, SIAM J. Numer. Anal., 39, 784-816) optimal error estimates were obtained for the lowest order case under the weaker hypothesis of the maximum angle con...
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paper:paper_02724979_v31_n4_p1683_Lombardi2023-06-08T15:25:18Z Interpolation error estimates for edge elements on anisotropic meshes Lombardi, Ariel L. anisotropic finite elements edge elements mixed finite elements The classical error analysis for Nédélec edge interpolation requires the so-called regularity assumption on the elements. However, in Nicaise (2001, SIAM J. Numer. Anal., 39, 784-816) optimal error estimates were obtained for the lowest order case under the weaker hypothesis of the maximum angle condition. This assumption allows for anisotropic meshes that become useful, for example, for the approximation of solutions with edge singularities. In this paper we prove optimal error estimates for the edge interpolation of any order under the maximum angle condition. We also obtain sharp stability results for that interpolation on appropriate families of elements. mixed finite elements; edge elements; anisotropic finite elements. © 2010 The author. Fil:Lombardi, A.L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2011 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02724979_v31_n4_p1683_Lombardi http://hdl.handle.net/20.500.12110/paper_02724979_v31_n4_p1683_Lombardi |
| 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 edge elements mixed finite elements |
| spellingShingle |
anisotropic finite elements edge elements mixed finite elements Lombardi, Ariel L. Interpolation error estimates for edge elements on anisotropic meshes |
| topic_facet |
anisotropic finite elements edge elements mixed finite elements |
| description |
The classical error analysis for Nédélec edge interpolation requires the so-called regularity assumption on the elements. However, in Nicaise (2001, SIAM J. Numer. Anal., 39, 784-816) optimal error estimates were obtained for the lowest order case under the weaker hypothesis of the maximum angle condition. This assumption allows for anisotropic meshes that become useful, for example, for the approximation of solutions with edge singularities. In this paper we prove optimal error estimates for the edge interpolation of any order under the maximum angle condition. We also obtain sharp stability results for that interpolation on appropriate families of elements. mixed finite elements; edge elements; anisotropic finite elements. © 2010 The author. |
| author |
Lombardi, Ariel L. |
| author_facet |
Lombardi, Ariel L. |
| author_sort |
Lombardi, Ariel L. |
| title |
Interpolation error estimates for edge elements on anisotropic meshes |
| title_short |
Interpolation error estimates for edge elements on anisotropic meshes |
| title_full |
Interpolation error estimates for edge elements on anisotropic meshes |
| title_fullStr |
Interpolation error estimates for edge elements on anisotropic meshes |
| title_full_unstemmed |
Interpolation error estimates for edge elements on anisotropic meshes |
| title_sort |
interpolation error estimates for edge elements on anisotropic meshes |
| publishDate |
2011 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02724979_v31_n4_p1683_Lombardi http://hdl.handle.net/20.500.12110/paper_02724979_v31_n4_p1683_Lombardi |
| work_keys_str_mv |
AT lombardiariell interpolationerrorestimatesforedgeelementsonanisotropicmeshes |
| _version_ |
1768544452077420544 |