Nonlinear advection problems and overlapping Schwarz waveform relaxation

Abstract

We analyze the convergence behavior of the overlapping Schwarz waveform relaxation algorithm applied to nonlinear advection problems. We show for Burgers' equation that the algorithm converges super-linearly at a rate which is asymptotically comparable to the rate of the algorithm applied to linear advection problems. The convergence rate depends on the overlap and the length of the time interval. We carefully track dependencies on the viscosity parameter and show the robustness of all estimates with respect to this parameter.