An Analysis of Higher Order Boundary Conditions for the Wave Equation

Abstract

Thanks to the use of the Cagniard--De Hoop method, we derive an analytic solution in the time domain for the half-space problem associated with the wave equation with Engquist--Majda higher order boundary conditions. This permits us to derive new convergence results when the order of the boundary condition tends to $+\infty$, as well as error estimates. The theory is illustrated by numerical results.