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A stabilized Nitsche overlapping mesh method for the Stokes problem
Simula Research Laboratory, Oslo, Norway.ORCID iD: 0000-0003-0803-9041
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Mathematical Sciences, Chalmers University of Technology, Gothenburg, Sweden.
Simula Research Laboratory, Oslo, Norway.
2014 (English)In: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 128, no 1, 73-101 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2014. Vol. 128, no 1, 73-101 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-93478DOI: 10.1007/s00211-013-0603-zISI: 000340590200003OAI: oai:DiVA.org:umu-93478DiVA: diva2:766904
Available from: 2014-11-28 Created: 2014-09-23 Last updated: 2017-12-05Bibliographically approved

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Massing, AndreLarson, Mats G.
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