Time domain Galerkin boundary elements provide an efficient tool for numerical solution of boundary value problems for the homogeneous wave equation. We review recent advances in their a~posteriori error analysis and the resulting adaptive mesh refinement procedures, as well as basic algorithmic aspects of these methods. Numerical results for adaptive mesh refinements are discussed in two and three dimensions, as are benchmark problems in a half-space related to the transient emission of traffic noise.
"Adaptive time domain boundary element methods with engineering applications." J. Integral Equations Applications 29 (1) 75 - 105, 2017. https://doi.org/10.1216/JIE-2017-29-1-75