Multiscale Petrov‐Galerkin FEM for Acoustic Scattering. Issue 1 (25th October 2016) - Gallistl, Dietmar; Peterseim, Daniel; Carstensen, Carsten
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 Q 1 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)