A MONOTONE MULTIDIMENSIONAL UPWIND FINITE-ELEMENT METHOD FOR ADVECTION-DIFFUSION PROBLEMS

We are interested in developing a multidimensional convective scheme t hat is capable of dealing with erroneous oscillations near jumps. The strategy is based on the Petrov-Galerkin formulation, to which the und erlying idea of the M matrix is added. The nature of the exponentially weighted upwind method is best illuminated by its matrix structure. W e interpret the enhanced stability as being due to the attainable irre ducible diagonal dominance. The accessible monotonicity condition enab les us to construct a monotone stiffness matrix a priori, thereby layi ng the foundation for arriving at the monotonicity-preserving property . In order to show the merit of the proposed upwinding technique in re solving spurious oscillations generated by unresolved internal and bou ndary layers, we considered two classes of convection-diffusion proble ms. As seen from rite computed results, we can attain an accurate fini te-element solation for a problem free of boundary layer and can captu re a high-gradient solution in the sharp layer.