Poroelasticity - gradient flow structures and iterative solvers (Jakub Both, University of Bergen)Séminaire « Analyse numérique et équations aux dérivées partielles »
Coupled flow in and deformation of porous media is highly relevant in many applications, ranging from subsurface to biomedical applications. In a broader sense, mathematically such processes are commonly described by coupling equations for linear elasticity and flow in porous media. In this talk, we discuss gradient flow structures for a class of poroelasticity models and how these can be utilized to derive robust iterative solvers. Applying iterative splitting schemes, incorporating decoupling of the respective subproblems, has become a widely-used approach to solve multi-physics problems. However, due to a saddle-point structure of poroelasticity (depending on the choice of primary variables) a naive approach quickly results in a non-robust solver. Numerical stabilization is required, and the presented procedure will provide both suitable choices for the stabilization, as well as a general approach for analyzing the convergence of the stabilized iterative coupling method.