A new weighted upwind finite volume element method based on non-standard covolume for time-dependent convection-diffusion problems
In modern numerical simulation of problems in energy resources and environmental science, it is important to develop efficient numerical methods for time-dependent convection-diffusion problems. On the basis of nonstandard covolume grids, we propose a new kind of high-order upwind finite volume element method for the problems. We first prove the stability and mass conservation in the discrete forms of the scheme. Optimal second-order error estimate in L-2-norm in spatial step is then proved strictly. The scheme is effective for avoiding numerical diffusion and nonphysical oscillations and has second-order accuracy. Numerical experiments are given to verify the performance of the scheme. Copyright (c) 2013 John Wiley & Sons, Ltd.
convection-diffusion nonstandard covolume stability mass conservation weighted upwind fvem high-order accuracy