## Interior penalty preconditioners for mixed finite element approximations of elliptic problems

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- by Torgeir Rusten, Panayot S. Vassilevski and Ragnar Winther PDF
- Math. Comp.
**65**(1996), 447-466 Request permission

## 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.## References

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## Additional Information

**Torgeir Rusten**- Affiliation: SINTEF, P. O. Box 124 Blindern, N-0314 Oslo, Norway
- Email: Torgeir.Rusten@si.sintef.no
**Panayot S. Vassilevski**- Affiliation: Center of Informatics and Computer Technology, Bulgarian Academy of Sciences, “Acad. G. Bontchev” street, Block 25 A, 1113 Sofia, Bulgaria
- Email: panayot@iscbg.acad.bg
**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): 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$\backslash$#415.
- © Copyright 1996 American Mathematical Society
- Journal: Math. Comp.
**65**(1996), 447-466 - MSC (1991): Primary 65F10, 65N20, 65N30
- DOI: https://doi.org/10.1090/S0025-5718-96-00720-X
- MathSciNet review: 1333325