This talk presents results from our recent efforts for reviving the 2-field (fluid pressure and solid displacement) approach for numerically solving poroelasticity problems on quadrilateral meshes. The Darcy equation is solved for fluid pressure by the weak Galerkin finite element methods, which establish the discrete weak gradient and numerical velocity in the Arbogast-Correa spaces.  The elasticity equation is solved for solid displacement by the enriched Lagrangian elements, which were motivated by the Bernardi-Raugel elements for Stokes flow. These two types of solvers are coupled through the implicit Euler temporal discretization to solve poroelasticity. Numerical experiments on two widely tested benchmarks will be presented to demonstrate the new solvers are locking-free. We discuss also extension to 3-dim and implementation in deal II. This is based on a series of joint work with several collaborators.

Jiangguo Liu earned a Ph.D. in Mathematics from University of South Carolina (USA) in 2001. He joined Colorado State University in 2005, where he is a now a Professor of Mathematics.  His research interests lie in numerical analysis, scientific computing, and mathematical biology.  He once served as the President of Central States Section of SIAM and is now serving as an associate editor for Journal of Computational and Applied Mathematics. He has published 50+ papers and been supported by US National Science Foundation on several research projects.