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Article Dans Une Revue Communications in Mathematical Sciences Année : 2022

Wavenumber explicit convergence analysis for finite element discretizations of time-harmonic wave propagation problems with perfectly matched layers

Résumé

The first part of this paper is devoted to a wavenumber-explicit stability analysis of a planar Helmholtz problem with a perfectly matched layer. We prove that, for a model scattering problem, the H1 norm of the solution is bounded by the right-hand side, uniformly in the wavenumber k in the highly oscillatory regime. The second part proposes two numerical discretizations: an hp finite element method and a multiscale method based on local subspace correction. The stability result is used to relate the choice of parameters in the numerical methods to the wavenumber. A priori error estimates are shown and their sharpness is assessed in numerical experiments.
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Dates et versions

hal-01887267 , version 1 (03-10-2018)

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Théophile Chaumont-Frelet, Dietmar Gallistl, Serge Nicaise, Jérôme Tomezyk. Wavenumber explicit convergence analysis for finite element discretizations of time-harmonic wave propagation problems with perfectly matched layers. Communications in Mathematical Sciences, 2022, 20 (1), pp.1-52. ⟨10.4310/CMS.2022.v20.n1.a1⟩. ⟨hal-01887267⟩
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