Multiscale Petrov‐Galerkin FEM for Acoustic Scattering. Issue 1 (25th October 2016)

• Record Type: Journal Article
• Authors: Gallistl, Dietmar; Peterseim, Daniel; Carstensen, Carsten
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 16:Issue 1(2016)
• Page Start: 745
• Page End: 746
• Publication Date: 2016-10-25
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201610361
• Languages: English
• ISSNs: 1617-7061

Abstract

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)