In this talk, we shall introduce the recent development regarding the pressure robust finite element method (FEM) for solving incompressible flow. We shall take the weak Galerkin (WG) scheme as the example to demonstrate the proposed enhancement technique in designing the robust numerical schemes and then illustrate the extension to other finite element methods. 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. Due to the viscosity and pressure 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. Then this method will be applied to solve several other incompressible fluid equations. We shall discuss the details in the implementation and theoretical analysis. Several numerical experiments will be tested to validate the theoretical conclusion.

Dr. Lin Mu is currently an assistant professor at the 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.