Paper presented at the 7th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Turkey, 19-21 July, 2010.
An explicit scheme based on a weighted mass matrix, for solving time-dependent convection-diffusion problems is studied. Convenient bounds for the time step, in terms of both the weights and the mesh step size, ensure its stability in the maximum norm, in both space and time, for piecewise linear finite element discretizations in any space dimension. Convergence results in the same sense also hold under certain conditions. The scheme is exploited numerically in order to illustrate its performance.