A weighted mass explicit scheme for convection-diffusion equations

An explicit scheme based on a weighted mass matrix, for solving time-dependent convection-diffusion problems was recently proposed by the author and collaborators. Convenient bounds for the time step, in terms of both the method's weights and the mesh step size, ensure its stability in space and time, for piecewise linear finite element discretisations in any space dimension. In this work we study some techniques for choosing the weights that guarantee the convergence of the scheme with optimal order in the space-time maximum norm, as both discretisation parameters tend to zero. Mathematical subject classification: Primary: 65M60; Secondary: 76Rxx.