Error estimates for Q1 isoparametric elements satisfying a weak angle condition
We prove optimal order error estimates in the H1 norm for the Q1 isoparametric interpolation on convex quadrilateral elements under rather weak hypotheses, improving previously known results. Choose one diagonal and divide the element into two triangles. We show that, if the chosen diagonal is the l...
Guardado en:
Autores principales: | , |
---|---|
Publicado: |
2001
|
Materias: | |
Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v38_n4_p1073_Acosta http://hdl.handle.net/20.500.12110/paper_00361429_v38_n4_p1073_Acosta |
Aporte de: |
id |
paper:paper_00361429_v38_n4_p1073_Acosta |
---|---|
record_format |
dspace |
spelling |
paper:paper_00361429_v38_n4_p1073_Acosta2023-06-08T15:01:58Z Error estimates for Q1 isoparametric elements satisfying a weak angle condition Acosta Rodriguez, Gabriel Duran, Ricardo Guillermo Anisotropic elements Isoparametric finite elements Lagrange interpolation Maximum angle condition Quadrilateral elements We prove optimal order error estimates in the H1 norm for the Q1 isoparametric interpolation on convex quadrilateral elements under rather weak hypotheses, improving previously known results. Choose one diagonal and divide the element into two triangles. We show that, if the chosen diagonal is the longest one, then the constant in the error estimate depends only on the maximum angle of the two triangles. Otherwise, the constant depends on that maximum angle and on the ratio between the two diagonals. In particular, we obtain the optimal order error estimate under the maximum angle condition as in the case of triangular elements. Consequently, the error estimate is uniformly valid for a rather general class of degenerate quadrilaterals. Fil:Acosta, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2001 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v38_n4_p1073_Acosta http://hdl.handle.net/20.500.12110/paper_00361429_v38_n4_p1073_Acosta |
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 Isoparametric finite elements Lagrange interpolation Maximum angle condition Quadrilateral elements |
spellingShingle |
Anisotropic elements Isoparametric finite elements Lagrange interpolation Maximum angle condition Quadrilateral elements Acosta Rodriguez, Gabriel Duran, Ricardo Guillermo Error estimates for Q1 isoparametric elements satisfying a weak angle condition |
topic_facet |
Anisotropic elements Isoparametric finite elements Lagrange interpolation Maximum angle condition Quadrilateral elements |
description |
We prove optimal order error estimates in the H1 norm for the Q1 isoparametric interpolation on convex quadrilateral elements under rather weak hypotheses, improving previously known results. Choose one diagonal and divide the element into two triangles. We show that, if the chosen diagonal is the longest one, then the constant in the error estimate depends only on the maximum angle of the two triangles. Otherwise, the constant depends on that maximum angle and on the ratio between the two diagonals. In particular, we obtain the optimal order error estimate under the maximum angle condition as in the case of triangular elements. Consequently, the error estimate is uniformly valid for a rather general class of degenerate quadrilaterals. |
author |
Acosta Rodriguez, Gabriel Duran, Ricardo Guillermo |
author_facet |
Acosta Rodriguez, Gabriel Duran, Ricardo Guillermo |
author_sort |
Acosta Rodriguez, Gabriel |
title |
Error estimates for Q1 isoparametric elements satisfying a weak angle condition |
title_short |
Error estimates for Q1 isoparametric elements satisfying a weak angle condition |
title_full |
Error estimates for Q1 isoparametric elements satisfying a weak angle condition |
title_fullStr |
Error estimates for Q1 isoparametric elements satisfying a weak angle condition |
title_full_unstemmed |
Error estimates for Q1 isoparametric elements satisfying a weak angle condition |
title_sort |
error estimates for q1 isoparametric elements satisfying a weak angle condition |
publishDate |
2001 |
url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v38_n4_p1073_Acosta http://hdl.handle.net/20.500.12110/paper_00361429_v38_n4_p1073_Acosta |
work_keys_str_mv |
AT acostarodriguezgabriel errorestimatesforq1isoparametricelementssatisfyingaweakanglecondition AT duranricardoguillermo errorestimatesforq1isoparametricelementssatisfyingaweakanglecondition |
_version_ |
1768544995013296128 |