An Analysis of the Weak Finite Element Method for Convection-Diffusion Equations
Numerical Analysis
2015-06-10 v1
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 -norm, the -norm and the -norm, respectively. In particular, the -superconvergence of order is given under certain condition. Finally, numerical examples are provided to illustrate our theoretical analysis
Cite
@article{arxiv.1506.02793,
title = {An Analysis of the Weak Finite Element Method for Convection-Diffusion Equations},
author = {Tie Zhang and Yanli Chen},
journal= {arXiv preprint arXiv:1506.02793},
year = {2015}
}