A Novel Cell-Centered Approach of Upwind Types for Convection Diffusion Equations on General Meshes

In this paper, we present novel cell-centered finite element methods for the convection-dominated convection–diffusion problems on the general meshes. The proposed schemes can be constructed from a general mesh by building with a dual mesh and its triangular sub-mesh. Moreover, the schemes are based on piecewise linear functions combined with two upwind techniques on the dual sub-mesh in order to stabilize the numerical solutions and eliminate the spurious oscillations. Through numerical results, two methods are shown to be effective in terms of accuracy, stability and computational cost.