Convergence Analysis of a Global-in-Time Iterative Decoupled Algorithm for Biot’s Model (Advances in Applied Mathematics and Mechanics, 2025)
Biot’s model is a multiphysics model that describes the interaction of a poroelastic material with its interstitial fluid flow. In this study, we focus on investigating the convergence behavior of a global-in-time iterative decoupled algorithm basedon a three-field formulation. During each iteration, the algorithm involves solving areaction-diffusion subproblem across the entire temporal domain, followed by resolving a Stokes subproblem over the same time interval. This algorithm is recognized forits ”partially parallel-in-time” property, enabling the implementation of a parallel procedure when addressing the Stokes subproblem. We establish its global convergencewith a new technique by confirming that the limit of the sequence of numerical solutions of the global-in-time algorithm is the numerical solution of the fully coupled algorithm. Numerical experiments validate the theoretical predictions and underline theefficiency gained by implementing the parallel procedure within the proposed global-in-time algorithm.