A NEW OVER-PENALIZED WEAK GALERKIN METHOD. PART III: CONVECTION-DIFFUSION-REACTION PROBLEMS

In this paper, we propose an over-penalized weak Galerkin (OPWG) finite element method for stationary convection-diffusion-reaction equations with full variable coefficients. This method employs piecewise polynomial ap-proximations of degree k (k = 1) for both the scalar function and its trace. Especially, the trace on inter-element boundaries is approximated by double-valued functions instead of single-valued ones. The (P-k, P-k, [Pk-1](d)) elements, with dimensions of space d = 2, 3 are employed. Our method deals with the convective term discretized in a trilinear form, and the uniqueness of numer-ical solutions is discussed. Optimal error estimates in the discrete H1-norm and L-2-norm are established, from which the optimal penalty exponent can be fixed. Numerical examples confirm the theory.