Maximum norm error estimators for three-dimensional elliptic problems

In this paper we define an a posteriori error estimator for finite element approximations of 3-d elliptic problems. We prove that the estimator is equivalent, up to logarithmic factors of the meshsize, to the maximum norm of the error. The results are valid for an arbitrary polyhedral domain and rat...

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Autores principales: Dari, E., Durán, R.G., Padra, C.
Formato: JOUR
Materias:
A posteriori
Adaptivity
Error estimators
Maximum norm
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00361429_v37_n2_p683_Dari
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00361429_v37_n2_p683_Dari
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spelling todo:paper_00361429_v37_n2_p683_Dari2023-10-03T14:47:42Z Maximum norm error estimators for three-dimensional elliptic problems Dari, E. Durán, R.G. Padra, C. A posteriori Adaptivity Error estimators Maximum norm In this paper we define an a posteriori error estimator for finite element approximations of 3-d elliptic problems. We prove that the estimator is equivalent, up to logarithmic factors of the meshsize, to the maximum norm of the error. The results are valid for an arbitrary polyhedral domain and rather general meshes. We also obtain analogous results for the nonconforming method of Crouzeix-Raviart. Finally, we present some numerical results comparing adaptive procedures based on controlling the error in different norms. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00361429_v37_n2_p683_Dari
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic A posteriori
Adaptivity
Error estimators
Maximum norm
spellingShingle A posteriori
Adaptivity
Error estimators
Maximum norm
Dari, E.
Durán, R.G.
Padra, C.
Maximum norm error estimators for three-dimensional elliptic problems
topic_facet A posteriori
Adaptivity
Error estimators
Maximum norm
description In this paper we define an a posteriori error estimator for finite element approximations of 3-d elliptic problems. We prove that the estimator is equivalent, up to logarithmic factors of the meshsize, to the maximum norm of the error. The results are valid for an arbitrary polyhedral domain and rather general meshes. We also obtain analogous results for the nonconforming method of Crouzeix-Raviart. Finally, we present some numerical results comparing adaptive procedures based on controlling the error in different norms.
format JOUR
author Dari, E.
Durán, R.G.
Padra, C.
author_facet Dari, E.
Durán, R.G.
Padra, C.
author_sort Dari, E.
title Maximum norm error estimators for three-dimensional elliptic problems
title_short Maximum norm error estimators for three-dimensional elliptic problems
title_full Maximum norm error estimators for three-dimensional elliptic problems
title_fullStr Maximum norm error estimators for three-dimensional elliptic problems
title_full_unstemmed Maximum norm error estimators for three-dimensional elliptic problems
title_sort maximum norm error estimators for three-dimensional elliptic problems
url http://hdl.handle.net/20.500.12110/paper_00361429_v37_n2_p683_Dari
work_keys_str_mv AT darie maximumnormerrorestimatorsforthreedimensionalellipticproblems
AT duranrg maximumnormerrorestimatorsforthreedimensionalellipticproblems
AT padrac maximumnormerrorestimatorsforthreedimensionalellipticproblems
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