Convergence properties and numerical simulation by an adaptive FEM of the thermistor problem

Claire Chauvin 1, 2, * Pierre Saramito 3 Christophe Trophime 4
* 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
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.
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Claire Chauvin, Pierre Saramito, Christophe Trophime. Convergence properties and numerical simulation by an adaptive FEM of the thermistor problem. 2007. 〈hal-00449960〉

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