The Costabel-Stephan system of Boundary Integral Equations in the Time Domain

Abstract: In this paper we formulate a transmission problem for the transient acoustic wave equation as a system of retarded boundary integral equations. We then analyse a fully discrete method using a general Galerkin semidiscretization-in-space and Convolution Quadrature in time. All proofs are developed using recent techniques based on the theory of evolution equations. Some numerical experiments are provided.