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Interior penalty preconditioners
for mixed finite element approximations
of elliptic problems

Authors: Torgeir Rusten, Panayot S. Vassilevski and Ragnar Winther
Journal: Math. Comp. 65 (1996), 447-466
MSC (1991): Primary 65F10, 65N20, 65N30
MathSciNet review: 1333325
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Abstract: It is established that an interior penalty method applied to second-order elliptic problems gives rise to a local operator which is spectrally equivalent to the corresponding nonlocal operator arising from the mixed finite element method. This relation can be utilized in order to construct preconditioners for the discrete mixed system. As an example, a family of additive Schwarz preconditioners for these systems is constructed. Numerical examples which confirm the theoretical results are also presented.

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Additional Information

Torgeir Rusten
Affiliation: SINTEF, P. O. Box 124 Blindern, N-0314 Oslo, Norway

Panayot S. Vassilevski
Affiliation: Center of Informatics and Computer Technology, Bulgarian Academy of Sciences, “Acad. G. Bontchev” street, Block 25 A, 1113 Sofia, Bulgaria

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

Keywords: Second-order elliptic\ problems, mixed finite elements, interior penalty preconditioners, domain decomposition
Received by editor(s): August 3, 1994
Received by editor(s) in revised form: November 29, 1994
Additional Notes: The work of all authors was partially supported by the Research Council of Norway (NFR), program no. 100998/420 and STP.29643. The work of the second author was also partially supported by the Bulgarian Ministry for Education, Science and Technology under grant MM-94$\$#415.
Article copyright: © Copyright 1996 American Mathematical Society