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A priori error analysis of space–time Trefftz discontinuous Galerkin methods for wave problems

Kretzschmar, F., Moiola, A., Perugia, I. and Schnepp, S. M. (2016) A priori error analysis of space–time Trefftz discontinuous Galerkin methods for wave problems. IMA Journal of Numerical Analysis, 36 (4). pp. 1599-1635. ISSN 1464-3642

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To link to this item DOI: 10.1093/imanum/drv064

Abstract/Summary

We present and analyse a space–time discontinuous Galerkin method for wave propagation problems. The special feature of the scheme is that it is a Trefftz method, namely that trial and test functions are solution of the partial differential equation to be discretised in each element of the (space–time) mesh. The method considered is a modification of the discontinuous Galerkin schemes of Kretzschmar et al. (2014) and of Monk & Richter (2005). For Maxwell’s equations in one space dimension, we prove stability of the method, quasi-optimality, best approximation estimates for polynomial Trefftz spaces and (fully explicit) error bounds with high order in the meshwidth and in the polynomial degree. The analysis framework also applies to scalar wave problems and Maxwell’s equations in higher space dimensions. Some numerical experiments demonstrate the theoretical results proved and the faster convergence compared to the non-Trefftz version of the scheme.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:45539
Publisher:Oxford University Press

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