Multiscale Petrov‐Galerkin FEM for Acoustic Scattering
Dietmar Gallistl, Daniel Peterseim, Carsten Carstensen · PAMM · 2016
Abstract We present a pollution‐free Petrov‐Galerkin multiscale finite element method for the Helmholtz problem with large wave number κ. We use standard continuous Q1 finite elements at a coarse discretization scale H as trial functions. The test functions are the solutions of local problems at a finer scale h. The diameter of the support of the test functions behaves like mH for some oversampling parameter m. Provided m is of the order of log(κ) and h is sufficiently small, the resulting method is stable and quasi‐optimal in the regime where H is proportional to κ−1. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)