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Penalty-free Nitsche method for interface problems

Boiveau, Thomas, Burman, Erik and Claus, Susanne 2017. Penalty-free Nitsche method for interface problems. Presented at: UCL Workshop 2016, London, UK, January 2016. Published in: Bordas, Stephane, Burman, Erik, Larson, Mats G. and Olshanskii, Maxim A. eds. Geometrically Unfitted Finite Element Methods and Applications. Lecture Notes in Computational Science and Engineering Cham: Springer, pp. 183-210. 10.1007/978-3-319-71431-8_6

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Nitsche’s method is a penalty-based method to weakly enforce boundary conditions in the finite element method. In this paper, we present a penalty free version of Nitsche’s method to impose interface coupling in the framework of unfitted domain decomposition. Unfitted domain decomposition is understood in the sense that the interface between the domains can cross elements of the mesh arbitrarily. The pure diffusion problem with discontinuous material parameters is considered for the theoretical study, we show the convergence of the L2 and H1-error for high contrast in the diffusivities. Then, we give the corresponding numerical results for the pure diffusion problem, additionally we consider the Stokes problem. We compare the performance of the penalty free method with the more classical symmetric and nonsymmetric Nitsche’s methods for different cases, including for the error generated in the interface fluxes.

Item Type: Conference or Workshop Item (Paper)
Date Type: Publication
Status: Published
Schools: Engineering
Publisher: Springer
ISBN: 9783319714301
ISSN: 1439-7358
Last Modified: 14 Dec 2020 02:21

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