The purpose of this presentation is to introduce basis concepts of the Weak Galerkin (WG) methods and their recent developments including new a posteriori estimators and applications on fluid dynamics. Weak Galerkin finite element methods are general methods for solving partial differential equations. The WG method is a natural extension of the standard Galerkin finite element method for the function with discontinuity since they have the same weak forms only where classical derivatives are substituted by weakly defined derivatives. Therefore, the weak Galerkin methods have the flexibility of employing discontinuous elements and, at the same time, share the simple formulations of continuous finite element methods.

叶秀, 阿肯色大学—小石城校区数学统计系教授, 目前已在国际知名期刊发表论文80余篇。她主要从事偏微分方程数值分析和科学计算方面的科研工作, 在所从事的领域具有一定得影响和成就。对偏微分方程中的有限体积元等方面取得重要结果。基于偏微分方程的求解问题, 叶秀教授最新提出了弱Galerkin有限元方法。