Finite Element Heterogeneous Multiscale Method for the Classical Helmholtz Equation

Patrick Ciarlet 1 Christian Stohrer 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 : We show that the standard Finite Element Heterogeneous Multiscale Method (FE-HMM) can be used to approximate the effective behavior of solutions to the classical Helmholtz equation in highly oscillatory media. Using a novel combination of well-known results about FE-HMM and the notion of T-coercivity, we derive an a priori error bound. Numerical experiments corroborate the analytical findings.
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Patrick Ciarlet, Christian Stohrer. Finite Element Heterogeneous Multiscale Method for the Classical Helmholtz Equation. Comptes Rendus Mathématique, Elsevier Masson, 2014, 352 (9), pp.755-760. ⟨10.1016/j.crma.2014.07.006⟩. ⟨hal-01111101⟩

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