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A Continuous Approach to FETI-DP Mortar Methods: Application to Dirichlet and Stokes Problem

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 91))

Summary

In this contribution we extend the FETI-DP mortar method for elliptic problems introduced by Bernardi et al. [2] and Chacón Vera [3] to the case of the incompressible Stokes equations showing that the same results hold in the two dimensional setting. These ideas extend easily to three dimensional problems. Finally some numerical tests are shown as a conclusion. This contribution is a condensed version of a more detailed forthcoming paper. We use standard notation, see for instance [1].

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Bibliography

  1. Robert A. Adams. Sobolev spaces. Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Pure and Applied Mathematics, Vol. 65.

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  2. C. Bernardi, T. Chacón Rebollo, and E. Chacón Vera. A FETI method with a mesh independent condition number for the iteration matrix. Comput. Methods Appl. Mech. Engrg., 197(13-16): 1410–1429, 2008. ISSN 0045-7825. doi: 10.1016/j.cma.2007.11.019. URL http://dx.doi.org/10.1016/j.cma.2007.11.019.

  3. Eliseo Chacón Vera. A continuous framework for FETI-DP with a mesh independent condition number for the dual problem. Comput. Methods Appl. Mech. Engrg., 198(30-32):2470–2483, 2009. ISSN 0045-7825. doi: 10.1016/j.cma.2009.02.037. URL http://dx.doi.org/10.1016/j.cma.2009.02.037.

  4. Vivette Girault and Pierre-Arnaud Raviart. Finite element methods for Navier-Stokes equations. Theory and algorithms., volume 5 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, 1986. ISBN 3-540-15796-4.

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  5. P. Grisvard. Singularities in boundary value problems, volume 22 of Recherches en Mathématiques Appliquées [Research in Applied Mathematics]. Masson, Paris, 1992. ISBN 2-225-82770-2.

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Acknowledgements

Research partially funded by Spanish government MEC Research Project MTM2009-07719. The authors thanks Frédéric Nataf and Tomás Chacón Rebollo for many valuable comments on this work.

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Correspondence to E. Chacón Vera .

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Vera, E.C., Coronil, D.F., Gavara, A.M. (2013). A Continuous Approach to FETI-DP Mortar Methods: Application to Dirichlet and Stokes Problem. In: Bank, R., Holst, M., Widlund, O., Xu, J. (eds) Domain Decomposition Methods in Science and Engineering XX. Lecture Notes in Computational Science and Engineering, vol 91. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35275-1_62

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