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Adaptive Refinement for $hp$-Version Trefftz Discontinuous Galerkin Methods for the Homogeneous Helmholtz Problem (1710.11427v1)
Published 31 Oct 2017 in math.NA
Abstract: In this article we develop an $hp$-adaptive refinement procedure for Trefftz discontinuous Galerkin methods applied to the homogeneous Helmholtz problem. Our approach combines not only mesh subdivision (h-refinement) and local basis enrichment (p-refinement), but also incorporates local directional adaptivity, whereby the elementwise plane wave basis is aligned with the dominant scattering direction. Numerical experiments based on employing an empirical a posteriori error indicator clearly highlight the efficiency of the proposed approach for various examples.