Abstract
We consider a space-time domain decomposition method based on Schwarz waveform relaxation (SWR) for the time-dependent Stokes–Darcy system. The coupled system is formulated as a time-dependent interface problem based on Robin–Robin transmission conditions, for which the decoupling SWR algorithm is proposed and proved for the convergence. In this approach, the Stokes and Darcy problems are solved independently and globally in time, thus allowing the use of different time steps for the local problems. Numerical tests are presented for both non-physical and physical problems with various mesh sizes and time step sizes to illustrate the accuracy and efficiency of the proposed method.
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