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Numerische Mathematik

, Volume 128, Issue 1, pp 73–101 | Cite as

A stabilized Nitsche overlapping mesh method for the Stokes problem

  • André Massing
  • Mats G. Larson
  • Anders Logg
  • Marie E. Rognes
Article

Abstract

We develop a Nitsche-based formulation for a general class of stabilized finite element methods for the Stokes problem posed on a pair of overlapping, non-matching meshes. By extending the least-squares stabilization to the overlap region, we prove that the method is stable, consistent, and optimally convergent. To avoid an ill-conditioned linear algebra system, the scheme is augmented by a least-squares term measuring the discontinuity of the solution in the overlap region of the two meshes. As a consequence, we may prove an estimate for the condition number of the resulting stiffness matrix that is independent of the location of the interface. Finally, we present numerical examples in three spatial dimensions illustrating and confirming the theoretical results.

Mathematics Subject Classification (2000)

65N12 65N30 76D07 

Notes

Acknowledgments

This work is supported by an Outstanding Young Investigator grant from the Research Council of Norway, NFR 180450. This work is also supported by a Center of Excellence grant from the Research Council of Norway to the Center for Biomedical Computing at Simula Research Laboratory.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • André Massing
    • 1
  • Mats G. Larson
    • 2
  • Anders Logg
    • 3
  • Marie E. Rognes
    • 1
  1. 1.Simula Research LaboratoryOsloNorway
  2. 2.Department of MathematicsUmeå UniversityUmeåSweden
  3. 3.Mathematical SciencesChalmers University of TechnologyGothenburgSweden

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