Space-time boundary elements on graded meshes for 3D elastodynamics

The solution to the elastodynamic equations in the exterior of a polygonal or polyhedral domain or a screen exhibits singularities at corners and edges. This paper presents a space-time boundary element method in 3D on algebraically graded meshes to resolve these singularities, based on recently obtained error estimates for the weakly singular integral equation. Numerical examples show the efficiency of the proposed approach. They confirm the theoretically predicted, quasi-optimal convergence rates and study the singular behavior of the solution for typical 3D geometries with edges, corners or cone points.