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.
Suggested Citation
Cai, Z., Parashkevov, R., Russell, T., Wilson, J.D., Ye, X., 2003, Domain decomposition for a mixed finite element method in three dimensions: SIAM Journal on Numerical Analysis, v. 41, no. 1, p. 181-194, https://doi.org/10.1137/S0036142996296935.
| 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 |