Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes

Hiptmair, R., Moiola, A. and Perugia, I. (2013) Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes. Applied Numerical Mathematics, 79. pp. 79-91. ISSN 0168-9274 doi: 10.1016/j.apnum.2012.12.004

Abstract/Summary

We extend the a priori error analysis of Trefftz-discontinuous Galerkin methods for time-harmonic wave propagation problems developed in previous papers to acoustic scattering problems and locally refined meshes. To this aim, we prove refined regularity and stability results with explicit dependence of the stability constant on the wave number for non convex domains with non connected boundaries. Moreover, we devise a new choice of numerical flux parameters for which we can prove L2-error estimates in the case of locally refined meshes near the scatterer. This is the setting needed to develop a complete hp-convergence analysis.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/30658
Identification Number/DOI	10.1016/j.apnum.2012.12.004
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Elsevier
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