Adaptive Refinement for $hp$-Version Trefftz Discontinuous Galerkin Methods for the Homogeneous Helmholtz Problem
Numerical Analysis
2017-11-01 v1
Abstract
In this article we develop an -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.
Cite
@article{arxiv.1710.11427,
title = {Adaptive Refinement for $hp$-Version Trefftz Discontinuous Galerkin Methods for the Homogeneous Helmholtz Problem},
author = {Scott Congreve and Paul Houston and Ilaria Perugia},
journal= {arXiv preprint arXiv:1710.11427},
year = {2017}
}