InterPore2022

A multipoint stress-flux mixed finite element method for the Stokes-Biot fluid poroelastic structure interaction model

1 Jun 2022, 14:05

15m

Oral Presentation (MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes MS07

Speaker

Ivan Yotov (University of Pittsburgh)

Description

We develop a fully mixed formulation of the Stokes-Biot model for fluid poroelastic structure interaction and its mixed finite element approximation. The Stokes formulation is based on weakly symmetric deviatoric stress, velocity, and vorticity. The elasticity formulation is based on weakly symmetric stress, displacement, and rotation. The porous media flow formulation is based on Darcy velocity and pressure. Well posedness of the variational formulation is established. The multipoint stress mixed finite element method is employed for the discretization of the Stokes and elasticity equations. The multipoint flux mixed finite element method is utilized for the Darcy flow. The methods are based on the lowest order BDM spaces for the stresses and the Darcy velocity. A vertex quadrature rule is employed for the bilinear forms involving these variables, which allows for their local elimination, as well as the local elimination of vorticity and rotation. This results in a symmetric and positive definite cell centered system involving only Stokes velocity, displacement, and pressure. We study the stability and accuracy of the method and present numerical experiments.

Presentation materials

yotov-interpore22.pdf