2025/04/24 by Botti, Michele, Prada, Daniele, Scotti, Anna +1 · 2 citations
#65M12 #65M60 #74F10 #76S05 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2504.17729
Poroelasticity describes the interaction of deformation and fluid flow in saturated porous media. A fully-mixed formulation of Biot's poroelasticity problem has the advantage of producing a better approximation of the Darcy velocity and stress field, as well as satisfying local mass and momentum conservation. In this work, we focus on a novel four-fields Virtual Element discretization of Biot's equations. The stress symmetry is strongly imposed in the definition of the discrete space, thus avoiding the use of an additional Lagrange multiplier. A complete a priori analysis is performed, showing the robustness of the proposed numerical method with respect to limiting material properties. The first order convergence of the lowest-order fully-discrete numerical method, which is obtained by coupling the spatial approximation with the backward Euler time-advancing scheme, is confirmed by a complete 3D numerical validation. A well known poroelasticity benchmark is also considered to assess the robustness properties and computational performance.