Convergent adaptive iterative schemes for solving multi-physics problems

In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive $\mathit{\text{a}}\mathit{\text{posteriori}}$ estimators to predict the success or failure of the method. Based on these estimators, we propose adaptive algorithms, including adaptively switching between methods, adaptive time-stepping methods, and the adaptive tuning of stabilization parameters. We apply this framework to two-phase flow in porous media, surfactant transport in porous media, and quasi-static poroelasticity.