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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Keywords Mass conservation, Poroelasticity equations, Stable finite elements
Persistent URL
Series Lecture Notes in Computer Science
Conference International Conference on Numerical Methods and Applications
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