Poroelasticity - gradient flow structures and iterative solvers (Jakub Both, University of Bergen)

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.