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arXiv · 1506.02793

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

Tie Zhang·Yanli Chen
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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

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Tie Zhang, Yanli Chen. 2015-06-09. An Analysis of the Weak Finite Element Method for Convection-Diffusion Equations. https://arxiv.org/abs/1506.02793

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