A Simplified Weak Galerkin Finite Element Method: Algorithm and Error Estimates
Numerical Analysis
2018-08-29 v2
Abstract
In this article a simplified weak Galerkin finite element method is developed for the Dirichlet boundary value problem of convection-diffusion-reaction equations. The simplified weak Galerkin method utilizes only the degrees of freedom on the boundary of each element and, hence, has significantly reduced computational complexity over the regular weak Galerkin finite element method. A stability and some optimal order error estimates in the and norms are established for the corresponding numerical solutions. Numerical results are presented to verify the theory error estimates and a superconvergence phenomena on rectangular partitions.
Cite
@article{arxiv.1808.08667,
title = {A Simplified Weak Galerkin Finite Element Method: Algorithm and Error Estimates},
author = {Yujie Liu and Junping Wang},
journal= {arXiv preprint arXiv:1808.08667},
year = {2018}
}