Monolithic, non-iterative and iterative time discretization methods for linear coupled elliptic-parabolic systems

Abstract

We compare four numerical methods for the time discretization of linear coupled elliptic-parabolic systems. The monolithic method arising from an implicit Euler discretization is the primary method for solving the coupled system. Accelerated solution via non-iterative decoupling is possible by the semi-explicit Euler discretization, using a novel methodology from related delay differential equations. For poroelasticity, the fixed-stress splitting and undrained splitting methods enable iterative decoupled solves. We present formulations for the iterative methods in an abstract form and compare through numerical experiments the a priori convergence results for the four methods.