An analysis of the weak Galerkin finite element method for convection–diffusion equations

摘要

We study the weak finite element method solving convection–diffusion equations. A new weak finite element scheme is presented based on a special variational form. The optimal order error estimates are derived in the discrete H1-norm, the L2-norm and the L∞-norm, respectively. In particular, the H1-superconvergence of order k+2 is obtained under certain condition if polynomial pair Pk(K)×Pk+1(∂K) is used in the weak finite element space. Finally, numerical examples are provided to illustrate our theoretical analysis.