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Domain decomposition for a mixed finite element method in three dimensions

SIAM Journal on Numerical Analysis

By:
, , , ,
DOI: 10.1137/S0036142996296935

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Abstract

We consider the solution of the discrete linear system resulting from a mixed finite element discretization applied to a second-order elliptic boundary value problem in three dimensions. Based on a decomposition of the velocity space, these equations can be reduced to a discrete elliptic problem by eliminating the pressure through the use of substructures of the domain. The practicality of the reduction relies on a local basis, presented here, for the divergence-free subspace of the velocity space. We consider additive and multiplicative domain decomposition methods for solving the reduced elliptic problem, and their uniform convergence is established.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Domain decomposition for a mixed finite element method in three dimensions
Series title:
SIAM Journal on Numerical Analysis
DOI:
10.1137/S0036142996296935
Volume
41
Issue:
1
Year Published:
2003
Language:
English
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
First page:
181
Last page:
194
Number of Pages:
14