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Substructure preconditioners for elliptic saddle point problems. (English) Zbl 0795.65072
Summary: 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.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
35J25 Boundary value problems for second-order elliptic equations
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