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The Recent Development of Weak Galerkin Finite Element Methods

发布者: bet体育      发布时间: 2021-07-10      浏览次数: 11bet体育

报告人: Dr. Lin Mu

报告时间: 2020年7月11日 上午9:00

报告方式: 腾讯会议 ID: 499 344 897

报告人及内容简介:

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.

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.


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