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arXiv · 1811.01595

hp-version time domain boundary elements for the wave equation on quasi-uniform meshes

Heiko Gimperlein·Ceyhun Oezdemir·David Stark·Ernst P. Stephan
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Abstract

Solutions to the wave equation in the exterior of a polyhedral domain or a screen in $\mathbb{R}^3$ exhibit singular behavior from the edges and corners. We present quasi-optimal $hp$-explicit estimates for the approximation of the Dirichlet and Neumann traces of these solutions for uniform time steps and (globally) quasi-uniform meshes on the boundary. The results are applied to an $hp$-version of the time domain boundary element method. Numerical examples confirm the theoretical results for the Dirichlet problem both for screens and polyhedral domains.

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Heiko Gimperlein, Ceyhun Oezdemir, David Stark, Ernst P. Stephan. 2018-11-05. hp-version time domain boundary elements for the wave equation on quasi-uniform meshes. https://doi.org/10.1016/j.cma.2019.07.018

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