Abstract
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.
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