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An adaptive NXFEM for the interface problem on locally refined triangular and quadrilateral meshes

Nelly Barrau 1, 2 R. Becker 1, 2 Eric Dubach 1, 2 Robert Luce 1 
2 CONCHA - Complex Flow Simulation Codes based on High-order and Adaptive methods
Inria Bordeaux - Sud-Ouest, UPPA - Université de Pau et des Pays de l'Adour, CNRS - Centre National de la Recherche Scientifique : UMR5142
Abstract : We propose an adaptive finite element method for the elliptic interface problem with piecewise constant coefficients, based on a robust variant of the original NXFEM of Hansbo and Hansbo [4], whitch allows for discontinuities, internal to the elements, in the approximation across the interface. This robust variant, introducing coefficients pondaration, provides constants in the error estimates independent of the geometry of the cut cells and also the coefficients. We extend the method to quadrilateral meshes and derive error estimators and perform several numerical tests.
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https://hal.inria.fr/hal-00864712
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Submitted on : Monday, September 23, 2013 - 10:27:48 AM
Last modification on : Friday, February 4, 2022 - 3:24:46 AM

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  • HAL Id : hal-00864712, version 1

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Nelly Barrau, R. Becker, Eric Dubach, Robert Luce. An adaptive NXFEM for the interface problem on locally refined triangular and quadrilateral meshes. ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, Sep 2012, Vienna, Austria. pp.3638-3646. ⟨hal-00864712⟩

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