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...

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Autores principales: Acosta, G., Durán, R.G.
Formato: JOUR
Materias:
Anisotropic elements
Isoparametric finite elements
Lagrange interpolation
Maximum angle condition
Quadrilateral elements
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00361429_v38_n4_p1073_Acosta
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00361429_v38_n4_p1073_Acosta2023-10-03T14:47:43Z Error estimates for Q1 isoparametric elements satisfying a weak angle condition Acosta, G. Durán, R.G. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, G.
Durán, R.G.
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.
format JOUR
author Acosta, G.
Durán, R.G.
author_facet Acosta, G.
Durán, R.G.
author_sort Acosta, G.
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
url http://hdl.handle.net/20.500.12110/paper_00361429_v38_n4_p1073_Acosta
work_keys_str_mv AT acostag errorestimatesforq1isoparametricelementssatisfyingaweakanglecondition
AT duranrg errorestimatesforq1isoparametricelementssatisfyingaweakanglecondition
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