In this talk we present two new formulations for elasticity and poromechanics that include rotations and total fluid-solid pressure as additional unknowns. We address the unique solvability of each problem and construct finite-element and finite-volume-element schemes for their numerical approximation. The stability and convergence of the methods are rigorously derived, and these results are of particular interest in the incompressible limit. We finally discuss how the formulations are modified when solving an interface problem defined by the coupling of an elastic and a poroelastic medium.

Ricardo did his PhD in Numerical Analysis in Concepcion, Chile in 2008. In 2009 he moved to EPFL where he was a Postdoc and later a Lecturer in Prof. Quarteroni's group until 2013. He then spent 2 years as a Senior Researcher at the Faculty of Earth Sciences in the University of Lausanne. Since 2015 he holds a Lectureship in Numerical Analysis at the Mathematical Institute of Oxford, where he is also involved in the doctoral programme on industrially-focused mathematical modelling.

Ricardo's research interests focus on the construction and theoretical analysis of mixed and hybrid numerical methods for coupled multiphysics problems. Recent applications include electromechanics of the heart, enhanced oil recovery models, sedimentation-consolidation processes in water waste treatment, and cross-diffusion effects in population dynamics.