Multiphysics Finite Element Methods for a Dynamic Poroelasticity Model
Prof. Xiaobing H. Feng(凤小兵)
University of Tennessee, USA
In this talk, I shall present some recent developments on multiphysics finite element methods for a poroelasticity model and for its limiting model (as the constrained storage coefficient tends to zero) which is known as Biot‘s consolidation problem in soil mechanics and is also known as Doi’s model for polymer gels. In particular, a new approach based on a multiphysics reformulation of the poroelasticity model will be discussed in detail. The idea of the approach is to introduce an “pseudo-pressure”and to show that such a pressure is governed by a diffusion process. Based on this new formulation various fully discrete finite element methods for approximating the model have been proposed and analyzed. A common feature of these methods is that at each time step two simple sub-problems need to be solved: one of which is a generalized Stokes-type problem for the displacement vector field and another is a diffusion problem for the “pseudo-pressure” field. The convergence and stability of these methods will be discussed and numerical experiment results will also be presented to demonstrate the efficiency of the approach, in particular, to show that the so-called “locking phenomenon” is naturally avoided.