Estimateurs d'erreur a posteriori pour des problèmes dynamiques

Abstract : In a first part, we introduce an a posteriori estimator for a nonconforming finite element approximation of the heat equation in R^d, d=2,3, using Backward Euler's scheme. For this discretization, we derive a residual indicator based on the jumps of the normal and tangential derivatives of the nonconforming approximation and a time residual based on the jump of broken gradients at each time step. Lower and upper bounds form the main results. We confirm the efficiency and reliability of these estimators. In a second part, we present an a posteriori estimator for the time dependent Stokes problem in R^d, d=2 or 3 Our analysis covers nonconforming finite element approximation (Crouzeix-Raviart's element). We derive an indicator which uses a spatial and time residual. Numerical experiments confirm the theoretical predictions and show the usefulness of these estimators on adaptive mesh refinement .
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Mathematics. Université de Valenciennes et du Hainaut-Cambresis, 2007. French


https://tel.archives-ouvertes.fr/tel-00156845
Contributor : Nadir Soualem <>
Submitted on : Friday, June 22, 2007 - 6:32:47 PM
Last modification on : Sunday, June 24, 2007 - 10:52:35 PM

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Nadir Soualem. Estimateurs d'erreur a posteriori pour des problèmes dynamiques. Mathematics. Université de Valenciennes et du Hainaut-Cambresis, 2007. French. <tel-00156845>

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