Ricardo Oyarzúa, Ricardo Ruiz-Baier:
Locking-free finite element methods for poroelasticity
We propose a new formulation along with a family of finite element schemes for the approximation of the interaction between fluid motion and linear mechanical response of a porous medium, known as the Biot consolidation problem. The system is recast in terms of displacement, pressure, and volumetric stress, and both continuous and discrete formulations are analyzed as compact perturbations of invertible problems employing a Fredholm argument. Numerical results indicate the satisfactory performance and competitive accuracy of the introduced methods.
This preprint gave rise to the following definitive publication(s):
Ricardo OYARZúA, Ricardo RUIZ-BAIER: Locking-free finite element methods for poroelasticity. SIAM Journal on Numerical Analysis, vol. 54, 5, pp. 2951-2973, (2016).