Kundan Kumar
University of Bergen, Bergen, Norway

Interaction of fluid such as CO$_2$ is of primary importance to evaluate the seismic hazard related to injection of fluids at depth. However, the role of fluid pressure in fault stability poses interesting challenges in our understanding of seismic events. We provide an overview of mathematical model describing flow and mechanics in the presence of fractures. The multiphysics model takes into account friction and normal forces including the effect of the fluid pressure. Using the methods of contact mechanics, we analyse the mathematical model and show the stability of solutions to small perturbations of the initial width of the fracture, fluid pressure, and the forcing term. Moreover, we consider temporal and spatial discretizations for numerically solving the governing equations. This is a joint work with Maarten de Hoop, Mircea Sofonea, Omar Duran, Solveig Stefansdottir, Mary Wheeler, and Vivette Girault.