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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
Published electronically: March 2, 1999
MathSciNet review: 1642817
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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 ${\boldsymbol{H}}(\operatorname{div})$-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: http://dx.doi.org/10.1090/S0025-5718-99-01076-5
PII: S 0025-5718(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