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A stabilized Nitsche fictitious domain formulation for the three-field Stokes problem
Department of Mathematics, University College London.
Department of Mathematics, University College London.
Center for Biomedical Computing at Simula Research Laboratory, P.O. Box 134, 1325 Lysaker.ORCID iD: 0000-0003-0803-9041
2013 (English)In: Proceeding of the 26th Nordic Seminar on Computational Mechanics / [ed] Anders Logg, Kent-Andre Mardal, Andre Massing, Simula Research Laboratory , 2013, p. 1-6Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

We propose a Nitsche fictitious domain method for the three-field Stokes problem where the dependent variables of velocity, pressure and extra-stress tensor are discretised with linear finite elements. To stabilise the equal order approximation, we employ a continuous interior penalty (CIP) method involving the normal gradient jumps of the velocity and pressure. On the unfitted boundary, Dirichlet boundary conditions are weakly enforced using Nitsche’s method. Adding CIP-like ghostpenalties in the vicinity of the boundary allows us to prove the inf-sup stability and optimal convergence of our method and to bound the condition number independent of the location of the boundary with respect to the computational mesh. Numerical examples corroborate the theoretical findings.

Place, publisher, year, edition, pages
Simula Research Laboratory , 2013. p. 1-6
Keywords [en]
Three-field Stokes, continuous interior penalty, fictitious domain, ghost penalty, Nitsche’s method
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-130967ISBN: 978-82-92593-12-7 (print)OAI: oai:DiVA.org:umu-130967DiVA, id: diva2:1070641
Conference
26th Nordic Seminar on Computational Mechanics, 23-25 October 2013, Oslo, Norway
Available from: 2017-02-01 Created: 2017-02-01 Last updated: 2018-06-09

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