Analysis of the parareal method with spectral deferred correction method for the Stokes/Darcy equations

Abstract

In this paper, we analyze a second-order numerical algorithm for the non-stationary mixed Stokes/Darcy equations with Beavers–Joseph–Saffman’s interface condition. The scheme is based on a finite element method in space and the parareal method with spectral deferred correction in time. We present the unconditional stability and the optimal error estimate of the full-discrete scheme. Finally, some numerical experiments are given to verify the effectiveness.