An Explicit Method for Convection-Diffusion Equations

Abstract

An explicit scheme for time-dependent convection-diffusion problems is presented. It is shown that convenient bounds for the time step value ensure $L^{\infty}$ stability, in both space and time, for piecewise linear finite element discretizations in any space dimension. Convergence results in the same sense are also demonstrated under certain conditions. Numerical results certify the good performance of the scheme.