%0 Journal Article %T An Analysis of the Weak Finite Element Method for Convection-Diffusion Equations %A Tie Zhang %A Yanli Chen %J Mathematics %D 2015 %I arXiv %X We study the weak finite element method solving convection-diffusion equations. A weak finite element scheme is presented based on a spacial variational form. We established a weak embedding inequality that is very useful in the weak finite element analysis. The optimal order error estimates are derived in the discrete $H^1$-norm, the $L_2$-norm and the $L_\infty$-norm, respectively. In particular, the $H^1$-superconvergence of order $k+2$ is given under certain condition. Finally, numerical examples are provided to illustrate our theoretical analysis %U http://arxiv.org/abs/1506.02793v1