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T-coercivity: Application to the discretization of Helmholtz-like problems

Patrick Ciarlet 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : To solve variational indefinite problems, a celebrated tool is the Banach-Ne?as-Babuška theory, which relies on the inf-sup condition. Here, we choose an alternate theory, T-coercivity. This theory relies on explicit inf-sup operators, both at the continuous and discrete levels. It is applied to solve Helmholtz-like problems in acoustics and electromagnetics. We provide simple proofs to solve the exact and discrete problems, and to show convergence under fairly general assumptions. We also establish sharp estimates on the convergence rates. © 2012 Elsevier Ltd. All rights reserved.
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Patrick Ciarlet. T-coercivity: Application to the discretization of Helmholtz-like problems. Computers and Mathematics with Applications, Elsevier, 2012, 64 (1), pp.22-34. ⟨10.1016/j.camwa.2012.02.034⟩. ⟨hal-00849560⟩



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