论文标题
一种弱的Galerkin方法及其两网格算法，用于非符号酮类型的准线性椭圆问题
A weak Galerkin method and its two-grid algorithm for the quasi-linear elliptic problems of non-monotone type
论文作者
论文摘要
在本文中，首先提出并分析了一种弱的彩色方法，并分析了非单线酮类型的准线性椭圆问题。通过使用Brouwer的固定点技术，得出了WG解决方案的存在以及类似于能量的标准和$ L^2 $ NORM中的错误估计。然后引入有效的两网络WG方法以提高计算效率。在能量样规范中分析了两个网格WG方法的收敛误差。提出了数值实验以验证我们的理论发现。
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 $L^2$ 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.
