skip to content
 

A four-field mixed finite element method for the Biot model and its solution algorithms

Presented by: 
Son-Young Yi University of Texas at El Paso
Date: 
Wednesday 8th June 2016 - 14:00 to 14:45
Venue: 
INI Seminar Room 1
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.


The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons