Veronica Anaya, Zoa De Wijn, Bryan Gomez-Vargas, David Mora, Ricardo Ruiz-Baier:
Rotation-based mixed formulations for an elasticity-poroelasticity interface problem
In this paper we introduce a new formulation for a stationary elasticity-poroelasticity problem written using rotations and total fluid-solid pressure as additional unknowns. The transmission conditions are imposed naturally in the weak formulation, and the analysis of the effective governing equations is conducted by an application of Fredholm's alternative. We also propose a monolithically coupled mixed finite element method for the numerical solution of the problem. Its convergence properties are rigorously derived, and subsequently confirmed by a set of computational tests that include applications to subsurface flow in reservoirs, and dentistry-oriented problems.
This preprint gave rise to the following definitive publication(s):
Veronica ANAYA, Zoa DE WIJN, Bryan GOMEZ-VARGAS, David MORA, Ricardo RUIZ-BAIER: Rotation-based mixed formulations for an elasticity-poroelasticity interface problem. SIAM Journal on Scientific Computing, vol. 42, 1, pp. B225–B249, (2020).