Efficient entropy stable Gauss collocation methods

Abstract

The construction of high order entropy stable collocation schemes on quadrilateral and hexahedral elements has relied on the use of Gauss-Legendre-Lobatto collocation points and their equivalence with summation-by-parts (SBP) finite difference operators. In this work, we show how to efficiently generalize the construction of semi-discretely entropy stable schemes on tensor product elements to Gauss points and generalized SBP operators. Numerical experiments suggest that the use of Gauss points significantly improves accuracy on curved meshes.

arXiv commentAccepted to SISC

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Cited by in corpus (4)

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• Stable discretisations of high-order discontinuous Galerkin methods on equidistant and scattered points
• Error boundedness of Correction Procedure via Reconstruction / Flux Reconstruction
• Skew-symmetric entropy stable modal discontinuous Galerkin formulations