Department of Mathematics

Applied Mathematics

  •  Jiangguo (James) Liu, Colorado State University
  •  Developing Finite Element Solvers for Poroelasticity in the Two-field Approach
  •  09/13/2019
  •  4:10 PM - 5:00 PM
  •  C304 Wells Hall

This talk presents results from our recent efforts for reviving the 2-field approach (fluid pressure and solid displacement) for numerically solving poroelasticity problems. We choose quadrilateral and hexahedral meshes for spatial discretization since they are equally flexible in accommodating complicated domain geometry but involve less unknowns, compared to simplicial meshes. The Darcy equation is solved for fluid pressure by the novel 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 finite elements are coupled through the implicit Euler temporal discretization to solve poroelasticity. Numerical experiments on benchmarks will be presented to show that the new solvers are locking-free. Implementation on deal.II will be discussed also. This talk is based on a series of joint work with several collaborators.



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science