Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem

Congreve, Scott and Houston, Paul and Perugia, Ilaria (2018) Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem. Advances in Computational Mathematics . ISSN 1572-9044 (In Press)

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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.

Item Type: Article
RIS ID: https://nottingham-repository.worktribe.com/output/946924
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1007/s10444-018-9621-9
Depositing User: Houston, Paul
Date Deposited: 22 Jun 2018 13:38
Last Modified: 04 May 2020 19:46
URI: http://eprints.nottingham.ac.uk/id/eprint/52555

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