We investigate a time-domain Galerkin boundary element method for the wave equation outside a Lipschitz obstacle in an absorbing half-space. A priori estimates are presented for both closed surfaces and screens, and we discuss the relevant properties of anisotropic Sobolev spaces and the boundary integral operators between them.
Gimperlein, H., Nehzi, Z., & Stephan, E. P. (2017). A priori error estimates for a time-dependent boundary element method for the acoustic wave equation in a half-space. Mathematical Methods in the Applied Sciences, 40(2), 448-462. https://doi.org/10.1002/mma.3340