Domain decomposition for a mixed finite element method in three dimensions
SIAM Journal on Numerical Analysis
By: Z. Cai, R.R. Parashkevov, T.F. Russell, J. D. Wilson, and X. Ye
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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.
| 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 |
| Larger Work Title | SIAM Journal on Numerical Analysis |
| First page | 181 |
| Last page | 194 |
| Google Analytic Metrics | Metrics page |