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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 prioridoi:10.4310/cms.2022.v20.n1.a1 fatcat:5uayg55z55cnnh6hgxatoptokq