Abstract

Co-author: Maranda L. Bean 

In this talk, I will present a four-field mixed finite element method for the 2D Biot’s consolidation model of poroelasticity. The method is based on coupling two mixed finite element methods for each subproblem: the standard mixed finite element method for the flow subproblem and the Hellinger-Reissner formulation for the mechanical subproblem. Optimal a-priori error estimates are proved for both semi-discrete and fully discrete problems.

In solving the coupled system, the two subproblems can be solved either simultaneously in a fully coupled scheme or sequentially in a loosely coupled scheme.  I will present four iteratively coupled methods, known as drained, undrained, fixed-strain, and fixed-stress splits, in which the diffusion operator is separated from the elasticity operator and the two subproblems are solved in a staggered way while ensuring convergence of the solution.  A-priori convergence results for each iterative coupling scheme will be proved and confirmed numerically.