Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version

Hiptmair, R., Moiola, A. and Perugia, I. (2016) Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version. Foundations of Computational Mathematics, 16 (3). pp. 637-675. ISSN 1615-3375 doi: 10.1007/s10208-015-9260-1

Abstract/Summary

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/40203
Identification Number/DOI	10.1007/s10208-015-9260-1
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Uncontrolled Keywords	Helmholtz equation Approximation by plane waves Trefftz-discontinuous Galerkin method hp h p -version A priori convergence analysis Exponential convergence 65N30 65N15 35J05
Publisher	Springer US
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