Preconditioners for higher order finite element discretizations of H(div)-elliptic problem

Preconditioners for higher order finite element discretizations of H(div)-elliptic problem

In this paper, we are concerned with the fast solvers for higher order finite element discretizations of H(div)-elliptic problem. We present the preconditioners for the first family and second family of higher order divergence conforming element equations, respectively. By combining the stable decompositions of two kinds of finite element spaces with the abstract theory of auxiliary space preconditioning, we prove that the corresponding condition numbers of our preconditioners are uniformly bounded on quasi-uniform grids.

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Main Authors: Wang,Junxian, Zhong,Liuqiang, Shu,Shi
Format: Digital revista
Language:English
Published: Sociedade Brasileira de Matemática Aplicada e Computacional 2010
Online Access:http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000100005
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spelling oai:scielo:S1807-030220100001000052010-03-19Preconditioners for higher order finite element discretizations of H(div)-elliptic problemWang,JunxianZhong,LiuqiangShu,Shi preconditioner higher order finite element stable decomposition H(div)-elliptic problem In this paper, we are concerned with the fast solvers for higher order finite element discretizations of H(div)-elliptic problem. We present the preconditioners for the first family and second family of higher order divergence conforming element equations, respectively. By combining the stable decompositions of two kinds of finite element spaces with the abstract theory of auxiliary space preconditioning, we prove that the corresponding condition numbers of our preconditioners are uniformly bounded on quasi-uniform grids.info:eu-repo/semantics/openAccessSociedade Brasileira de Matemática Aplicada e ComputacionalComputational & Applied Mathematics v.29 n.1 20102010-01-01info:eu-repo/semantics/articletext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000100005en10.1590/S1807-03022010000100005
institution SCIELO
collection OJS
country Brasil
countrycode BR
component Revista
access En linea
databasecode rev-scielo-br
tag revista
region America del Sur
libraryname SciELO
language English
format Digital
author Wang,Junxian
Zhong,Liuqiang
Shu,Shi
spellingShingle Wang,Junxian
Zhong,Liuqiang
Shu,Shi
Preconditioners for higher order finite element discretizations of H(div)-elliptic problem
author_facet Wang,Junxian
Zhong,Liuqiang
Shu,Shi
author_sort Wang,Junxian
title Preconditioners for higher order finite element discretizations of H(div)-elliptic problem
title_short Preconditioners for higher order finite element discretizations of H(div)-elliptic problem
title_full Preconditioners for higher order finite element discretizations of H(div)-elliptic problem
title_fullStr Preconditioners for higher order finite element discretizations of H(div)-elliptic problem
title_full_unstemmed Preconditioners for higher order finite element discretizations of H(div)-elliptic problem
title_sort preconditioners for higher order finite element discretizations of h(div)-elliptic problem
description In this paper, we are concerned with the fast solvers for higher order finite element discretizations of H(div)-elliptic problem. We present the preconditioners for the first family and second family of higher order divergence conforming element equations, respectively. By combining the stable decompositions of two kinds of finite element spaces with the abstract theory of auxiliary space preconditioning, we prove that the corresponding condition numbers of our preconditioners are uniformly bounded on quasi-uniform grids.
publisher Sociedade Brasileira de Matemática Aplicada e Computacional
publishDate 2010
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000100005
work_keys_str_mv AT wangjunxian preconditionersforhigherorderfiniteelementdiscretizationsofhdivellipticproblem
AT zhongliuqiang preconditionersforhigherorderfiniteelementdiscretizationsofhdivellipticproblem
AT shushi preconditionersforhigherorderfiniteelementdiscretizationsofhdivellipticproblem
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