Here, we treat mathematical and practical aspects of poroelastic models, with an emphasis on their stable discretization and the highly efficient solution of the resulting algebraic systems, which are of saddle point type. Standard poroelastic models couple the equations of elastic deformation of a porous body with the effects of pressure from a fluid within the pores. However, this problem can interact with other different models to explain a more complex phenomenon describing more complicated multiphysics problems. Nowadays, poroelastic models are used to study problems in many diverse areas as geomechanics, hydrogeology, petrol engineering, biomechanics, etc. Therefore, the study of this type of problems is of great interest to scientists and engineers.

Francisco José Gaspar received his Mathematics degree in 1989 at the University of Zaragoza. He obtained his PhD with distinction at the University of Oviedo in 1997. Currently, he is Professor in the Department of Applied Mathematics at the University of Zaragoza. He is associate editor of the Journal "Mathematical Modelling and Analysis" and he has been invited editor in other three different journals. As well, he is member of the scientific committee of several international conferences. His research interests lie within the framework of the numerical analysis for partial differential equations. He is mainly interested in the theoretical and practical study of multigrid methods and in the