Error estimates for a partially penalized immersed finite element method for elasticity interface problems

Guo, Ruchi; Lin, Tao; Lin, Yanping

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 1, pp. 1-24.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

This article is about the error analysis for a partially penalized immersed finite element (PPIFE) method designed to solve linear planar-elasticity problems whose Lamé parameters are piecewise constants with an interface-independent mesh. The bilinear form in this method contains penalties to handle the discontinuity in the global immersed finite element (IFE) functions across interface edges. We establish a stress trace inequality for IFE functions on interface elements, we employ a patch idea to derive an optimal error bound for the stress of the IFE interpolation on interface edges, and we design a suitable energy norm by which the bilinear form in this PPIFE method is coercive. These key ingredients enable us to prove that this PPIFE method converges optimally in both an energy norm and the usual L² norm under the standard piecewise H²-regularity assumption for the exact solution. Features of the proposed PPIFE method are demonstrated with numerical examples.

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