Numerical Analysis
A robust variant of NXFEM for the interface problem
Comptes Rendus. Mathématique, Volume 350 (2012) no. 15-16, pp. 789-792.

In this note, we propose a modification of the NXFEM proposed in Hansbo and Hansbo (2002) [4] for the elliptic interface problem. It leads to a robust method not only with respect to the mesh-interface geometry, but also with respect to the diffusion parameters.

Dans cette note, nous proposons une modification de NXFEM proposée dans Hansbo et Hansbo (2002) [4] pour le problème dʼinterface elliptique. Elle permet dʼobtenir la robuste à la fois par rapport à la géometrie du maillage coupé par lʼinterface et par rapport aux paramètres de diffusion.

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Published online:
DOI: 10.1016/j.crma.2012.09.018
Barrau, Nelly 1; Becker, Roland 1; Dubach, Eric 1; Luce, Robert 1

1 Equipe Concha, Université de Pau and INRIA Bordeaux Sud-Ouest, 64013 Pau cedex, France
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Barrau, Nelly; Becker, Roland; Dubach, Eric; Luce, Robert. A robust variant of NXFEM for the interface problem. Comptes Rendus. Mathématique, Volume 350 (2012) no. 15-16, pp. 789-792. doi : 10.1016/j.crma.2012.09.018. http://www.numdam.org/articles/10.1016/j.crma.2012.09.018/

[1] Becker, R.; Burman, E.; Hansbo, P. A hierarchical NXFEM for fictitious domain simulations, Int. J. Numer. Meth. Engrg., Volume 86 (2011), pp. 549-559

[2] Burman, E.; Hansbo, P. Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method, Appl. Numer. Math., Volume 62 (2012), pp. 328-341

[3] Ern, A.; Stephansen, A.F.; Zunino, P. A discontinuous Galerkin method with weighted averages for advection–diffusion equations with locally small and anisotropic diffusivity, IMA J. Numer. Anal., Volume 29 (2009), pp. 235-256

[4] Hansbo, A.; Hansbo, P. An unfitted finite element method, based on Nitscheʼs method, for elliptic interface problems, Comput. Methods Appl. Mech. Eng., Volume 191 (2002), pp. 5537-5552

[5] Hansbo, A.; Hansbo, P.; Larson, M.G. A finite element method on composite grids based on Nitscheʼs method, ESAIM, Math. Model. Numer. Anal., Volume 37 (2003), pp. 495-514

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