Adaptive and higher-order time domain boundary elements for the wave equation

Abstract: 

We present h and p-versions of the time domain boundary element method for boundary and screen problems for the wave equation in 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.

This is a joint with H. Gimperlein and D. Stark, Heriot-Watt University, Edinburgh, UK.