Substructure preconditioners for elliptic saddle point problems

Authors:
Torgeir Rusten and Ragnar Winther

Journal:
Math. Comp. **60** (1993), 23-48

MSC:
Primary 65N55; Secondary 65F10, 65N30, 76S05

DOI:
https://doi.org/10.1090/S0025-5718-1993-1149293-0

MathSciNet review:
1149293

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Abstract: Domain decomposition preconditioners for the linear systems arising from mixed finite element discretizations of second-order elliptic boundary value problems are proposed. The preconditioners are based on subproblems with either Neumann or Dirichlet boundary conditions on the interior boundary. The preconditioned systems have the same structure as the nonpreconditioned systems. In particular, we shall derive a preconditioned system with conditioning independent of the mesh parameter *h*. The application of the minimum residual method to the preconditioned systems is also discussed.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1993-1149293-0

Keywords:
Second-order elliptic equations,
mixed finite element methods,
domain decomposition

Article copyright:
© Copyright 1993
American Mathematical Society