Finite-element heterogeneous multiscale method for the Helmholtz equation

Patrick Ciarlet; Christian Stohrer

doi:10.1016/j.crma.2014.07.006

Finite-element heterogeneous multiscale method for the Helmholtz equation

Patrick Ciarlet, Christian Stohrer

Laboratoire POems UMR 7231 CNRS-INRIA-ENSTA, ENSTA-UMA

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	755-760
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	352
Issue number	9
DOIs	https://doi.org/10.1016/j.crma.2014.07.006
Publication status	Published - 1 Sept 2014

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title = "Finite-element heterogeneous multiscale method for the Helmholtz equation",

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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AU - Stohrer, Christian

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AB - 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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DO - 10.1016/j.crma.2014.07.006

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SN - 1631-073X

VL - 352

SP - 755

EP - 760

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 9

ER -

Finite-element heterogeneous multiscale method for the Helmholtz equation

Abstract

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