Preconditioning for Mixed Finite Element Formulations of Elliptic Problems

Tim Wildey; Guangri Xue

doi:10.1007/978-3-642-35275-1_19

Preconditioning for Mixed Finite Element Formulations of Elliptic Problems

Tim Wildey, Guangri Xue

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

2 Scopus citations

Abstract

In this paper, we discuss a preconditioning technique for mixed finite element discretizations of elliptic equations. The technique is based on a block-diagonal approximation of the mass matrix which maintains the sparsity and positive definiteness of the corresponding Schur complement. This preconditioner arises from the multipoint flux mixed finite element method and is robust with respect to mesh size and is better conditioned for full permeability tensors than a preconditioner based on a diagonal approximation of the mass matrix. © Springer-Verlag Berlin Heidelberg 2013.

Original language	English (US)
Title of host publication	Domain Decomposition Methods in Science and Engineering XX
Publisher	Springer Nature
Pages	175-182
Number of pages	8
ISBN (Print)	9783642352744
DOIs	https://doi.org/10.1007/978-3-642-35275-1_19
State	Published - May 9 2013
Externally published	Yes

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10.1007/978-3-642-35275-1_19

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title = "Preconditioning for Mixed Finite Element Formulations of Elliptic Problems",

abstract = "In this paper, we discuss a preconditioning technique for mixed finite element discretizations of elliptic equations. The technique is based on a block-diagonal approximation of the mass matrix which maintains the sparsity and positive definiteness of the corresponding Schur complement. This preconditioner arises from the multipoint flux mixed finite element method and is robust with respect to mesh size and is better conditioned for full permeability tensors than a preconditioner based on a diagonal approximation of the mass matrix. {\textcopyright} Springer-Verlag Berlin Heidelberg 2013.",

author = "Tim Wildey and Guangri Xue",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-F1-032-04 Acknowledgements: Guangri Xue is supported by Award No. KUS-F1-032-04, made by KingAbdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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AU - Xue, Guangri

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-F1-032-04 Acknowledgements: Guangri Xue is supported by Award No. KUS-F1-032-04, made by KingAbdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2013/5/9

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N2 - In this paper, we discuss a preconditioning technique for mixed finite element discretizations of elliptic equations. The technique is based on a block-diagonal approximation of the mass matrix which maintains the sparsity and positive definiteness of the corresponding Schur complement. This preconditioner arises from the multipoint flux mixed finite element method and is robust with respect to mesh size and is better conditioned for full permeability tensors than a preconditioner based on a diagonal approximation of the mass matrix. © Springer-Verlag Berlin Heidelberg 2013.

AB - In this paper, we discuss a preconditioning technique for mixed finite element discretizations of elliptic equations. The technique is based on a block-diagonal approximation of the mass matrix which maintains the sparsity and positive definiteness of the corresponding Schur complement. This preconditioner arises from the multipoint flux mixed finite element method and is robust with respect to mesh size and is better conditioned for full permeability tensors than a preconditioner based on a diagonal approximation of the mass matrix. © Springer-Verlag Berlin Heidelberg 2013.

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BT - Domain Decomposition Methods in Science and Engineering XX

PB - Springer Nature

ER -

Preconditioning for Mixed Finite Element Formulations of Elliptic Problems

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