A domain embedding preconditioner for the Lagrange multiplier system
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- by Einar Haug and Ragnar Winther PDF
- Math. Comp. 69 (2000), 65-82 Request permission
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 ${\mathbfit {H}}(\operatorname {div})$–inner product, for the block of the preconditioner corresponding to the multipliers.References
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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
- MR Author ID: 183665
- Email: Ragnar.Winther@ifi.uio.no
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Math. Comp. 69 (2000), 65-82
- MSC (1991): Primary 65F10, 65N22, 65N30
- DOI: https://doi.org/10.1090/S0025-5718-99-01076-5
- MathSciNet review: 1642817