Weak Galerkin Finite Element Methods and Numerical Applications

October 11, 2018

Thursday, October 11, 2018
Dr. Lin Mu
Oak Ridge National Lab
2:00 - 3:00pm
SEH, B1220

 

Abstract

Weak Galerkin FEMs are new numerical methods that were first introduced for solving general second order elliptic PDEs. The differential operators are replaced by their weak discrete derivatives, which endows high flexibility in developing high order numerical schemes on the polytonal meshes and naturally handling meshes with hanging nodes. This new method is a discontinuous finite element algorithm, which is parameter-free, symmetric and absolutely stable. In this talk, we will discuss about the novel weak Galerkin finite element methods to discretize the PDEs and analyze the a priori and a posteriori error estimate accordingly. Efficient implementation and robustness of our approach technique will be investigated. Furthermore, the fully computable a posteriori error estimate gives a reliable estimate for the interested error and thus can be used for guiding further refinement for singularity involved problems.
 

Biography

Dr. Lin Mu is currently a householder fellow working at ORNL. Dr. Mu received her Ph.D. in Applied Science from the University of Arkansas in 2013 and her M.Sc. in Computational Mathematics from Xi'an Jiaotong University in 2009. 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 methods and Efficient Numerical Solver of Mathematical techniques to chemistry, biology and material sciences.