An Optimal-Order Error Estimate to the Modified Method of Characteristics for a Degenerate Convection-Diffusion Equation

Abstract

We prove a priori error estimates in a weighted energy norm to the modified method of characteristics (MMOC) for time-dependent convection-diffusion equations with degenerate diffusion. The convergence rates are independent of the lower bound of the diffusion. In other words, these estimates hold uniformly with respect to the degenerate diffusion.