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

Théophile Chaumont-Frelet, Dietmar Gallistl, Serge Nicaise, Jérôme Tomezyk
2022 Communications in Mathematical Sciences  
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 H 1 norm of the solution is bounded by the right-hand side, uniformly in the wavenumber k in the high wavenumber regime. The second part proposes two numerical discretizations, namely, a high-order finite element method and a multiscale method based on local subspace correction. We establish a priori
more » ... rror estimates, based on the aforementioned stability result, that permit to properly select the discretization parameters with respect to the wavenumber. Numerical experiments assess the sharpness of our key results.
doi:10.4310/cms.2022.v20.n1.a1 fatcat:5uayg55z55cnnh6hgxatoptokq