## June 6 – Ivan Yotov: Coupled multipoint flux and multipoint stress mixed finite element methods for poroelasticity

Ivan Yotov: Tuesday 6 June at 11 am, A415 Inria Paris. We discuss mixed finite element approximations for the Biot system of poroelasticity. We employ a weak stress symmetry elasticity formulation with three fields – stress, displacement, and rotation, as well as a mixed velocity-pressure Darcy formulation. The method is reduced to a cell-centered scheme for the displacement and the pressure, using the multipoint flux mixed finite element method for flow and the recently developed multipoint stress mixed finite element method for elasticity. The methods utilize the Brezzi-Douglas-Marini spaces for velocity and stress and a trapezoidal-type quadrature rule for integrals involving velocity, stress, and rotation, which allows for local flux, stress, and rotation elimination. We perform stability and error analysis and present numerical experiments illustrating the convergence of the method and its performance for modeling flows in deformable reservoirs. This is joint work with Ilona Ambartsumyan and Eldar Khattatov, University of Pittsburgh.