An Analysis of the Weak Finite Element Method for Convection-Diffusion Equations

Abstract

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

References in corpus (1)

• A Computational Study of the Weak Galerkin Method for Second-Order Elliptic Equations