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arXiv · 1910.07315

A space-time hybridizable discontinuous Galerkin method for linear free-surface waves

Giselle Sosa Jones·Jeonghun J. Lee·Sander Rhebergen
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Abstract

We present and analyze a novel space-time hybridizable discontinuous Galerkin (HDG) method for the linear free-surface problem on prismatic space-time meshes. We consider a mixed formulation which immediately allows us to compute the velocity of the fluid. In order to show well-posedness, our space-time HDG formulation makes use of weighted inner products. We perform an a priori error analysis in which the dependence on the time step and spatial mesh size is explicit. We provide two numerical examples: one that verifies our analysis and a wave maker simulation.

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Giselle Sosa Jones, Jeonghun J. Lee, Sander Rhebergen. 2019-10-16. A space-time hybridizable discontinuous Galerkin method for linear free-surface waves. https://doi.org/10.1007/s10915-020-01340-8

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