A space-time hybridizable discontinuous Galerkin method for linear free-surface waves
Numerical Analysis
2023-07-06 v1 Numerical Analysis
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.
Cite
@article{arxiv.1910.07315,
title = {A space-time hybridizable discontinuous Galerkin method for linear free-surface waves},
author = {Giselle Sosa Jones and Jeonghun J. Lee and Sander Rhebergen},
journal= {arXiv preprint arXiv:1910.07315},
year = {2023}
}