论文标题
较弱的彩色元素的数值研究
Numerical investigation on weak Galerkin finite elements
论文作者
论文摘要
弱伽勒金（WG）有限元方法是一种用于求解部分微分方程的有效且灵活的一般数值技术。薄弱的galerkin有限元方法的新思想是使用弱功能及其定义为分布的弱衍生物。弱功能和弱衍生物可以通过不同程度的多项式近似。多项式空间的不同组合会产生不同的弱绿色有限元。本文的目的是通过提供31张表中记录的许多数值实验来研究不同WG元素的稳定性，收敛性和超细度。这些表有两个目的。首先，它提供了不同WG元素的性能的详细指南。其次，表格中的信息打开了新的研究领域，为什么某些WG元素表现优于其他元素。
The weak Galerkin (WG) finite element method is an effective and flexible general numerical technique for solving partial differential equations. The novel idea of weak Galerkin finite element methods is on the use of weak functions and their weak derivatives defined as distributions. Weak functions and weak derivatives can be approximated by polynomials with various degrees. Different combination of polynomial spaces generates different weak Galerkin finite elements. The purpose of this paper is to study stability, convergence and supercloseness of different WG elements by providing many numerical experiments recorded in 31 tables. These tables serve two purposes. First it provides a detail guide of the performance of different WG elements. Second, the information in the tables opens new research territory why some WG elements outperform others.
