In this paper, we present and analyze a weak Galerkin finite element (WG) method for solving the symmetric hyperbolic systems . This method is highlyflexible by allowing the use of discontinuous finite elements on element and boundary independently of each other . Numerical examples are provided to show the effectiveness of the proposed WG method . As application, wediscuss this WG way for solving singularly perturbedconvection-diffusion-reaction equation and derive an $\varepsilon$-uniformerror estimate of order \$k+1/2 .

Author(s) : Tie Zhang, Shangyou Zhang