In this work, we consider two discretizations of the three-field formulation of Biot’s consolidation problem. They employ the lowest-order mixed finite elements for the flow (Raviart-Thomas-Nédélec elements for the Darcy velocity and piecewise constants for the pressure) and are stable with respect to the physical parameters. The difference is in the mechanics: one of the discretizations uses Crouzeix-Raviart nonconforming linear elements; the other is based on piecewise linear elements stabilized by using face bubbles, which are subsequently eliminated. The numerical solutions obtained from these discretizations satisfy mass conservation: the former directly and the latter after a simple postprocessing.

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Lecture Notes in Computer Science
International Conference on Numerical Methods and Applications
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Gaspar, F.J, Rodrigo, C, Hu, X, Ohm, P, Adler, J.H, & Zikatanov, L.T. (2019). New stabilized discretizations for poroelasticity equations. In Lecture Notes in Computer Science/Lecture Notes in Artificial Intelligence (pp. 3–14). doi:10.1007/978-3-030-10692-8_1