Title: The Recent Development of Weak Galerkin Finite Element Methods

Speaker: Lin Mu, Department of Mathematics, University of Georgia

Time：2020.11.28, 10:00-12:00am

Tencent Meeting（腾讯会议）：705 797 393

Abstract:  

In this talk, we shall introduce the recent development regarding the weak Galerkin finite element method (FEM). Weak Galerkin (WG) Method is a natural extension of the classical Galerkin finite element method with advantages in many aspects. For example, due to its high structural flexibility, the weak Galerkin finite element method is well suited to most partial differential equations on the general meshing by providing the needed stability and accuracy. In this talk, the speaker shall discuss the new divergence preserving schemes and upwind stabilization techniques in designing the robust numerical schemes. Due to the viscosity independence in the velocity approximation, our scheme is robust with small viscosity and/or large permeability, which tackles the crucial computational challenges in fluid simulation. For the convection dominate flow, we shall employ the upwind scheme and the effective WENO limiter treatment to derive the spurious oscillation free solutions. Several numerical experiments will be tested to validate the theoretical conclusion.

Bio for Lin Mu:

Dr. Lin Mu is currently an assistant professor at Department of Mathematics, University of Georgia. Before moving to UGA, she was a householder fellow working at ORNL. Dr. Mu received her Ph.D. in Applied Science from the University of Arkansas in 2012 and her M.Sc. and B.S in Computational Mathematics from Xi'an Jiaotong University in 2009 and 2006. Dr. Mu's areas of interest include: Applied Mathematics, Numerical Analysis and Scientific Computing; Theory and Application of Finite Element Methods, Adaptive Methods, Post-processing approach; Multiscale Modeling approach and Efficient Numerical Solver to engineering, chemistry, biology and material sciences.

报告人中文简介：

    穆琳，陕西省西安人，博士，现任美国佐治亚大学助理教授。2006年本科毕业于西安交通大学信息与计算科学系，2006年保送西安交通大学数学系攻读硕士学位，研究生导师是何银年教授，2009年进入阿肯色大学小石城分校，师从叶秀教授攻读博士学位，2012年获博士学位并被职美国密歇根大学聘为客座助理教授，2015年至2019年于美国橡树岭国家实验室任职，并于2019年入职美国佐治亚大学。主要研究方向包括，应用数学，数值分析，科学计算；有限元方法的理论分析和应用；自适应方法，后处理方法；多尺度计算和高效的数值计算格式。