In this talk, we shall introduce the recent development regarding the pressure robust weak Galerkin finite element method (FEM) for solving incompressible flow. 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 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. We shall discuss the details in the implementation and theoretical analysis. Several numerical experiments will be tested to validate the theoretical conclusions.

References:
1. L. Mu. Pressure Robust Weak Galerkin Finite Element Methods for Stokes Problems. SIAM Journal on Scientific Computing, 42 (2020), B608–B629. 
2. L. Mu. A Uniformly Robust H(div) Weak Galerkin Finite Element Methods for Brinkman Problems. SIAM Journal on Numerical Analysis, 58 (2020), 1422–1439. 

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.