Robin-Robin domain decomposition methods for fluid-poroelastic structure interaction
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We develop domain decomposition methods for the Stokes-Biot model of fluid-poroelastic structure interaction based on Robin-Robin transmission conditions. The Robin data is modeled as an auxiliary variable. We study a non-iterative time-splitting method that requires one Stokes and one Biot solve per time step. We establish unconditional stability and convergence in time with rate $O(\sqrt{\Delta t})$. We further consider an iterative coupling method that involves an iteration between the Stokes and Biot subproblems at each time step and establish convergence to the monolithic solution. Numerical results are presented to illustrate the theory.
