Finite element approximations in a nonlipschitz domain

In this paper we analyze the approximation by standard piecewise linear finite elements of a nonhomogeneous Neumann problem in a cuspidal domain. Since the domain is not Lipschitz, many of the results on Sobolev spaces, which are fundamental in the usual error analysis, do not apply. Therefore, we n...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Acostat, G., Armentano, M.G., Durán, R.G., Lombardi, A.L.
Formato: JOUR
Materias:
Cuspidal domains
Finite elements
Graded meshes
Neumann problem
Error analysis
Finite element method
Problem solving
Approximation algorithms
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00361429_v45_n1_p277_Acostat
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00361429_v45_n1_p277_Acostat
record_format dspace
spelling todo:paper_00361429_v45_n1_p277_Acostat2023-10-03T14:47:44Z Finite element approximations in a nonlipschitz domain Acostat, G. Armentano, M.G. Durán, R.G. Lombardi, A.L. Cuspidal domains Finite elements Graded meshes Neumann problem Error analysis Finite element method Problem solving Cuspidal domains Graded meshes Neumann problem Approximation algorithms In this paper we analyze the approximation by standard piecewise linear finite elements of a nonhomogeneous Neumann problem in a cuspidal domain. Since the domain is not Lipschitz, many of the results on Sobolev spaces, which are fundamental in the usual error analysis, do not apply. Therefore, we need to work with weighted Sobolev spaces and to develop some new theorems on traces and extensions. We show that, in the domain considered here, suboptimal order can be obtained with quasi-uniform meshes even when the exact solution is in H 2, and we prove that the optimal order with respect to the number of nodes can be recovered by using appropriate graded meshes. © 2007 Society for Industrial and Applied Mathematics. Fil:Armentano, M.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. Fil:Lombardi, A.L. 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_v45_n1_p277_Acostat
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Cuspidal domains
Finite elements
Graded meshes
Neumann problem
Error analysis
Finite element method
Problem solving
Cuspidal domains
Graded meshes
Neumann problem
Approximation algorithms
spellingShingle Cuspidal domains
Finite elements
Graded meshes
Neumann problem
Error analysis
Finite element method
Problem solving
Cuspidal domains
Graded meshes
Neumann problem
Approximation algorithms
Acostat, G.
Armentano, M.G.
Durán, R.G.
Lombardi, A.L.
Finite element approximations in a nonlipschitz domain
topic_facet Cuspidal domains
Finite elements
Graded meshes
Neumann problem
Error analysis
Finite element method
Problem solving
Cuspidal domains
Graded meshes
Neumann problem
Approximation algorithms
description In this paper we analyze the approximation by standard piecewise linear finite elements of a nonhomogeneous Neumann problem in a cuspidal domain. Since the domain is not Lipschitz, many of the results on Sobolev spaces, which are fundamental in the usual error analysis, do not apply. Therefore, we need to work with weighted Sobolev spaces and to develop some new theorems on traces and extensions. We show that, in the domain considered here, suboptimal order can be obtained with quasi-uniform meshes even when the exact solution is in H 2, and we prove that the optimal order with respect to the number of nodes can be recovered by using appropriate graded meshes. © 2007 Society for Industrial and Applied Mathematics.
format JOUR
author Acostat, G.
Armentano, M.G.
Durán, R.G.
Lombardi, A.L.
author_facet Acostat, G.
Armentano, M.G.
Durán, R.G.
Lombardi, A.L.
author_sort Acostat, G.
title Finite element approximations in a nonlipschitz domain
title_short Finite element approximations in a nonlipschitz domain
title_full Finite element approximations in a nonlipschitz domain
title_fullStr Finite element approximations in a nonlipschitz domain
title_full_unstemmed Finite element approximations in a nonlipschitz domain
title_sort finite element approximations in a nonlipschitz domain
url http://hdl.handle.net/20.500.12110/paper_00361429_v45_n1_p277_Acostat
work_keys_str_mv AT acostatg finiteelementapproximationsinanonlipschitzdomain
AT armentanomg finiteelementapproximationsinanonlipschitzdomain
AT duranrg finiteelementapproximationsinanonlipschitzdomain
AT lombardial finiteelementapproximationsinanonlipschitzdomain
_version_ 1782027565256409088

Ejemplares similares