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 and norms are derived for the corresponding characteristics weak Galerkin finite element procedure. Numerical tests are performed and reported.
Ailing Zhu. Qiang Xu. Ziwen Jiang. "Characteristics Weak Galerkin Finite Element Methods for Convection-Dominated Diffusion Problems." Abstr. Appl. Anal. 2014 (SI13) 1 - 8, 2014. https://doi.org/10.1155/2014/102940