A domain embedding preconditioner

for the Lagrange multiplier system

Authors:
Einar Haug and Ragnar Winther

Journal:
Math. Comp. **69** (2000), 65-82

MSC (1991):
Primary 65F10, 65N22, 65N30

DOI:
https://doi.org/10.1090/S0025-5718-99-01076-5

Published electronically:
March 2, 1999

MathSciNet review:
1642817

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Abstract | References | Similar Articles | Additional Information

Abstract: Finite element approximations for the Dirichlet problem associated to a second-order elliptic differential equation are studied. The purpose of this paper is to discuss domain embedding preconditioners for discrete systems. The essential boundary condition on the interior interface is removed by introducing Lagrange multipliers. The associated discrete system, with a saddle point structure, is preconditioned by a block diagonal preconditioner. The main contribution of this paper is to propose a new operator, constructed from the -inner product, for the block of the preconditioner corresponding to the multipliers.

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Additional Information

**Einar Haug**

Affiliation:
SINTEF, P. O. Box 124 Blindern, N–0314 Oslo, Norway

Email:
Einar.Haug@math.sintef.no

**Ragnar Winther**

Affiliation:
Department of Informatics, University of Oslo, P. O. Box 1080 Blindern, N–0316 Oslo, Norway

Email:
Ragnar.Winther@ifi.uio.no

DOI:
https://doi.org/10.1090/S0025-5718-99-01076-5

Keywords:
Second--order elliptic problems,
Dirichlet boundary conditions,
Lagrange multiplier method,
preconditioning,
domain embedding

Received by editor(s):
March 26, 1997

Received by editor(s) in revised form:
March 17, 1998

Published electronically:
March 2, 1999

Additional Notes:
This work was partially supported by the Research Council of Norway (NFR), program no. 100998/420 and STP.29643

Article copyright:
© Copyright 1999
American Mathematical Society