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A stabilized Nitsche overlapping mesh method for the Stokes problem

A. Massing ; M. G. Larson ; Anders Logg (Institutionen för matematiska vetenskaper, matematik) ; M. E. Rognes
Numerische Mathematik (0029-599X). Vol. 128 (2014), 1, p. 73-101.
[Artikel, refereegranskad vetenskaplig]

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.


Denna post skapades 2014-10-20. Senast ändrad 2014-10-20.
CPL Pubid: 204581


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