Our new preprint on Accurate Discretization Of Poroelasticity Without Darcy Stability — Stokes-Biot Stability Revisited is now out on arXiv!
What is the right concept of Stokes-Biot stability? The Stokes, Darcy and Biot equations are partial differential equations describing viscous fluid flow, flow in a porous medium, and flow in a poroelastic medium, respectively. Numerical discretizations of the Biot equations are notoriously prone to instabilities and numerical artifacts. In response, Stokes-Biot stability has been introduced as a concept for ensuring Biot stability and convergence even for the challenging cases of low permeabilities and low storage coefficients. The original definition of Stokes-Biot stability relies on both Stokes and Darcy stability. However, ensuring Darcy stability can be highly non-trivial. In this note, we point at how the Darcy stability condition can be relaxed. This allows for a new stability concept: minimal Stokes-Biot stability.