Convergence properties and numerical simulation by an adaptive FEM of the thermistor problemReport as inadecuate




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* Corresponding author 1 MOISE - Modelling, Observations, Identification for Environmental Sciences Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble 2 TOSCA INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502 3 EDP - Equations aux Dérivées Partielles LJK - Laboratoire Jean Kuntzmann 4 LCMI-GHMFL - Laboratoire des champs magnétiques intenses

Abstract : In this paper, the convergence properties of the finite element approximation of the thermistor problem are investigated, both from theoretical and numerical point of view. From one hand, based on a duality argument, a theoretical convergence result is proved under low regularity assumption. From other hand, numerical experiments are performed based on a decoupled algorithm. Moreover, on a non convex domain, the convergence properties versus the mesh size are shown to be improved by using suitable mesh adaptation strategy and error estimator.

Keywords : mesh adaptation Thermistor problem L1 right-hand-side existence result convergence of the finite element method corner singularity mesh adaptation.





Author: Claire Chauvin - Pierre Saramito - Christophe Trophime -

Source: https://hal.archives-ouvertes.fr/



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