First order system least squares pseudo-spectral method for Stokes-Darcy equations

The subject of this paper is to investigate the first order system least squares Legendre and Chebyshev pseudo-spectral methods for coupled Stokes-Darcy equations. By introducing strain tensor as a new variable, Stokes-Darcy equations recast into a system of first order differential equations. The least squares functional is defined by summing up the weighted L2-norm of residuals of the first order system for coupled Stokes-Darcy equations. To treat Beavers-Joseph-Saffman interface conditions, the weighted L2-norm of these conditions are also added to the least squares functional. Continuous and discrete homogeneous functionals are shown to be equivalent to the combination of weighted H(div) and H1-norm for Stokes-Darcy equations. The spectral convergence for the Legendre and Chebyshev methods are derived. To demonstrate this analysis, numerical experiments are also presented.