Robust estimates for the approximation of the dynamic consolidation problem

Abstract

Abstract. We consider stable discretizations in time and space for the linear dynamic consolidation problem describing the wave propagation in a porous solid skeleton which is fully saturated with an incompressible uid. Introducing the hydrostatic pressure, the ow problem is described by Darcy's law. In particular, we discuss the case of nearly impermeable solids which requires inf-sup stable discretizations in space for the limiting saddle point problem. Together with an (implicit) Newmark discretization in time we derive convergence estimates for the fully discrete scheme which are robust with respect to the coupling parameter of uid and solid.

A Method of Fundamental Solutions in Poroelasticity to Model the Stress Field in Geothermal Reservoirs

“…Stability results in the context of quasistatic thermoelasticity can be found in [231] and (for a finite element formulation) for dynamic poroelasticity in [245] and the references therein. However, the time derivative of the pressure is omitted in [245].…”