Leibniz University Hannover, with H. Gimperlein, D. Stark (Heriot-Watt University, Edinburgh) and C.Oezdemir (LUH)
Adaptive and higher-order time domain boundary elements for the wave equation
We present $h$ and $p$-versions of the time domain boundary element method for boundary and screen problems for the wave equation in $\mathbb{R}^3$. First, graded meshes are shown to recover optimal approximation rates for solution in the presence of edge and corner singularities on screens. Then an a posteriori error estimate is presented for general discretizations, and it gives rise to adaptive mesh refinement procedures. We also discuss preliminary results for $p$ and $hp$-versions of the time domain boundary element method. Numerical experiments illustrate the theory.
