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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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
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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Keywords: Second-order elliptic equations, mixed finite element methods, domain decomposition
Article copyright: © Copyright 1993 American Mathematical Society