Sílvia Barbeiro (Universidade de Coimbra)

Coupling methods for poroelasticity

Poroelasticity modeling attracts  researchers from different areas and is of  great importance not only in soil mechanics but also in several applications in civil,  petroleum and even biomedical engineering. In this talk we consider the numerical solution of a coupled fluid flow and geomechanics in Biot's consolidation model for poroelasticity. The method combines mixed finite elements for Darcy flow and Galerkin finite elements for elasticity. The numerical discretization of this model gives rise to algorithmic challenges. Our focus is to discuss the development  of efficient and accurate numerical solutions, and give some insight into the theoretical basis of the underlying methods. The fully coupled approach solves flow and elasticity equations simultaneously. Alternatively, operator splitting techniques can be used for solving the discrete system. The choice of the coupling scheme affects the stability and accuracy of the numerical solutions as well as the computational efficiency. In this talk we discuss a priori convergence estimates for fully coupled schemes  and for iteratively coupled schemes. We perform numerical experiments for verifying our theory and to compare different coupling techniques in  engineering applications.