Auxiliary space preconditioners for mixed finite element methods

Ray S. Tuminaro; Jinchao Xu; Yunrong Zhu

doi:10.1007/978-3-642-02677-5_9

Auxiliary space preconditioners for mixed finite element methods

Ray S. Tuminaro, Jinchao Xu, Yunrong Zhu

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

9 Scopus citations

Abstract

This paper is devoted to study of an auxiliary spaces preconditioner for H(div) systems and its application in the mixed formulation of second order elliptic equations. Extensive numerical results show the efficiency and robustness of the algorithms, even in the presence of large coefficient variations. For the mixed formulation of elliptic equations, we use the augmented Lagrange technique to convert the solution of the saddle point problem into the solution of a nearly singular H(div) system. Numerical experiments also justify the robustness and efficiency of this scheme. © 2009 Springer-Verlag Berlin Heidelberg.

Original language	English (US)
Title of host publication	Lecture Notes in Computational Science and Engineering
Pages	99-109
Number of pages	11
DOIs	https://doi.org/10.1007/978-3-642-02677-5_9
State	Published - Oct 12 2009
Externally published	Yes

ASJC Scopus subject areas

General Engineering
Modeling and Simulation
Computational Mathematics
Discrete Mathematics and Combinatorics
Control and Optimization

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10.1007/978-3-642-02677-5_9

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title = "Auxiliary space preconditioners for mixed finite element methods",

abstract = "This paper is devoted to study of an auxiliary spaces preconditioner for H(div) systems and its application in the mixed formulation of second order elliptic equations. Extensive numerical results show the efficiency and robustness of the algorithms, even in the presence of large coefficient variations. For the mixed formulation of elliptic equations, we use the augmented Lagrange technique to convert the solution of the saddle point problem into the solution of a nearly singular H(div) system. Numerical experiments also justify the robustness and efficiency of this scheme. {\textcopyright} 2009 Springer-Verlag Berlin Heidelberg.",

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AU - Xu, Jinchao

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PY - 2009/10/12

Y1 - 2009/10/12

N2 - This paper is devoted to study of an auxiliary spaces preconditioner for H(div) systems and its application in the mixed formulation of second order elliptic equations. Extensive numerical results show the efficiency and robustness of the algorithms, even in the presence of large coefficient variations. For the mixed formulation of elliptic equations, we use the augmented Lagrange technique to convert the solution of the saddle point problem into the solution of a nearly singular H(div) system. Numerical experiments also justify the robustness and efficiency of this scheme. © 2009 Springer-Verlag Berlin Heidelberg.

AB - This paper is devoted to study of an auxiliary spaces preconditioner for H(div) systems and its application in the mixed formulation of second order elliptic equations. Extensive numerical results show the efficiency and robustness of the algorithms, even in the presence of large coefficient variations. For the mixed formulation of elliptic equations, we use the augmented Lagrange technique to convert the solution of the saddle point problem into the solution of a nearly singular H(div) system. Numerical experiments also justify the robustness and efficiency of this scheme. © 2009 Springer-Verlag Berlin Heidelberg.

UR - http://link.springer.com/10.1007/978-3-642-02677-5_9

UR - http://www.scopus.com/inward/record.url?scp=78651556446&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-02677-5_9

DO - 10.1007/978-3-642-02677-5_9

M3 - Conference contribution

SN - 9783642026768

SP - 99

EP - 109

BT - Lecture Notes in Computational Science and Engineering

ER -

Auxiliary space preconditioners for mixed finite element methods

Abstract

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