A novel iterative time integration scheme for linear poroelasticity

Abstract

Within this paper, we introduce and analyze a novel time-stepping scheme for linear poroelasticity. In each time frame, we iteratively solve the flow and mechanics equations with an additional damping step for the pressure variable. Depending on the coupling strength of the two equations, we explicitly quantify the required number of inner iteration steps to guarantee first-order convergence. By a number of numerical experiments we confirm the theoretical results and study the dependence of the inner iteration steps in terms of the coupling strength. Moreover, we compare our method to the well-known fixed-stress scheme.