A novel convergence analysis of Robin–Robin domain decomposition method for Stokes–Darcy system with Beavers–Joseph interface condition

Abstract

In this paper, we demonstrate the convergence analysis of Robin–Robin domain decomposition method with finite element discretization for Stokes–Darcy system with Beavers-Joseph interface condition, with particular attention paid to the case which is convergent for small viscosity and hydraulic conductivity in practice. Based on the techniques of the discrete harmonic extension and discrete Stokes extension, the convergence is proved and the almost optimal geometric convergence rate is obtained for the case of γf>γp. Here γf and γp are positive Robin parameters introduced in Cao et al., 2011, which was not able to show the analysis for γf>γp but only numerically illustrated its importance to the convergence for the practical situation with small viscosity and hydraulic conductivity. The analysis result provides a general guideline of choice on the relevant parameters to obtain the convergence and geometric convergence rate. The numerical results verify the theoretical conclusion.