A weak Galerkin method and its two-grid algorithm for the quasi-linear elliptic problems of non-monotone type
Numerical Analysis
2022-07-07 v2 Numerical Analysis
Abstract
In this article, a weak Galerkin method is firstly presented and analyzed for the quasi-linear elliptic problem of non-monotone type. By using Brouwer's fixed point technique, the existence of WG solution and error estimates in both the energy-like norm and the norm are derived. Then an efficient two-grid WG method is introduced to improve the computational efficiency. The convergence error of the two-grid WG method is analyzed in the energy-like norm. Numerical experiments are presented to verify our theoretical findings.
Cite
@article{arxiv.2202.11164,
title = {A weak Galerkin method and its two-grid algorithm for the quasi-linear elliptic problems of non-monotone type},
author = {Peng Zhu and Shenglan Xie},
journal= {arXiv preprint arXiv:2202.11164},
year = {2022}
}
Comments
26 pages, 4 figures