A New Combined Finite Element-Upwind Finite Volume Method for the Convection-Dominated Diffusion Problems

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In this article, we develop a combined finite element-weighted upwind finite volume method for convection-dominated diffusion problems in two dimensions, which discretizes the diffusion term with the standard finite element scheme, and the convection and source terms with the weighted upwind finite volume scheme. The developed method leads to a totally new scheme for convection-dominated problems, which overcomes numerical oscillation, avoids numerical dispersion, and has high-order accuracy. Stability analyses of the scheme are given for the problems with constant coefficients. Numerical experiments are presented to illustrate the stability and optimal convergence of our proposed method.