Solutions to the wave equation in the exterior of a polyhedral domain or a screen in R3 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.
|Number of pages||30|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|Early online date||23 Jul 2019|
|Publication status||Published - 1 Nov 2019|