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hp-version time domain boundary elements for the wave equation on quasi-uniform meshes (1811.01595v3)
Published 5 Nov 2018 in math.NA and cs.NA
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.