Characteristics Weak Galerkin Finite Element Methods for Convection-Dominated Diffusion Problems

Abstract

The weak Galerkin finite element method is combined with the method of characteristics to treat the convection-diffusion problems on the triangular mesh. The optimal order error estimates in $H^1$ and $L^2$ norms are derived for the corresponding characteristics weak Galerkin finite element procedure. Numerical tests are performed and reported.