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T-coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients

Lucas Chesnel 1 Patrick Ciarlet 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : To solve variational indefinite problems, one uses classically the Banach-Necas-Babuška theory. Here, we study an alternate theory to solve those problems: T-coercivity. Moreover, we prove that one can use this theory to solve the approximate problems, which provides an alternative to the celebrated Fortin lemma. We apply this theory to solve the indefinite problem $div\sigma\nabla u = f$ set in $H^1_0$, with $\sigma$ exhibiting a sign change.
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Submitted on : Wednesday, April 18, 2012 - 4:33:20 PM
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Lucas Chesnel, Patrick Ciarlet. T-coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients. 2012. ⟨hal-00688862⟩

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