Multiscale Petrov-Galerkin FEM for acoustic scattering

D. Gallistl, D. Peterseim, C. Carstensen

Research output: Contribution to journalConference articleAcademicpeer-review


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
Original languageEnglish
Pages (from-to)745-746
Number of pages2
JournalProceedings in Applied Mathematics and Mechanics
Issue number1
Publication statusPublished - 2016
Externally publishedYes
Event87th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) and Deutsche Mahematiker-Vereinigung (DMV) 2016 - Braunschweig, Germany
Duration: 7 Mar 201611 Mar 2016
Conference number: 87


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