AuthorsA. Massing, M. G. Larson, A. Logg and M. E. Rognes
TitleA Stabilized Nitsche Overlapping Mesh Method for the Stokes Problem
AfilliationBiomedical Computing, Center for Biomedical Computing (SFF), Scientific Computing
Project(s)Center for Biomedical Computing (SFF)
StatusPublished
Publication TypeJournal Article
Year of Publication2014
JournalNumerische Mathematik
Volume128
Issue1
Numberonline
Pagination73-101
Date PublishedJanuary
Publisher
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.

DOI10.1007/s00211-013-0603-z
Citation KeySimula.simula.2502