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A Nitsche cut finite element method for the Oseen problem with general Navier boundary conditions
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2018 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 330, p. 220-252Article in journal (Refereed) Published
Abstract [en]

In this work a Nitsche-based imposition of generalized Navier conditions on cut meshes for the Oseen problem is presented. Other methods from literature dealing with the generalized Navier condition impose this condition by means of substituting the tangential Robin condition in a classical Galerkin way. These methods work fine for a large slip length coefficient but lead to conditioning and stability issues when it approaches zero. We introduce a novel method for the weak imposition of the generalized Navier condition which remains well-posed and stable for arbitrary choice of slip length, including zero. The method proposed here builds on the formulation done by Juntunen and Stenberg (2009). They impose a Robin condition for the Poisson problem by means of Nitsche's method for an arbitrary combination of the Dirichlet and Neumann parts of the condition. The analysis conducted for the proposed method is done in a similar fashion as in Massing et al. (2018), but is done here for a more general type of boundary condition. The analysis proves stability for all flow regimes and all choices of slip lengths. Also an L-2-optimal estimate for the velocity error is shown, which was not conducted in the previously mentioned work. A numerical example is carried out for varying slip lengths to verify the robustness and stability of the method with respect to the choice of slip length. Even though proofs and formulations are presented for the more general case of an unfitted grid method, they can easily be reduced to the simpler case of a boundary-fitted grid with the removal of the ghost-penalty stabilization terms 

Place, publisher, year, edition, pages
ELSEVIER SCIENCE SA , 2018. Vol. 330, p. 220-252
Keywords [en]
Oseen problem, General Navier boundary condition, Cut finite element method, Nitsche's method, ip boundary condition, Navier-Stokes equations
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-145769DOI: 10.1016/j.cma.2017.10.023ISI: 000425735700010OAI: oai:DiVA.org:umu-145769DiVA, id: diva2:1192469
Available from: 2018-03-22 Created: 2018-03-22 Last updated: 2018-06-09Bibliographically approved

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Massing, Andre

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