LEAST SQUARES SPECTRAL METHOD FOR VELOCITY-FLUX FORM OF THE COUPLED STOKES-DARCY EQUATIONS

Abstract

This paper develops least squares Legendre and Chebyshev spectral methods for the first order system of Stokes-Darcy equations. The least squares functional is based on the velocity-flux-pressure formulation with the enforcement of the Beavers-Joseph-Saffman interface conditions. Continuous and discrete homogeneous functionals are shown to be equivalent to the combination of weighted H1H1 and H(div)H(div)-norm for the Stokes and Darcy equations. The spectral convergence for the Legendre and Chebyshev methods are derived and numerical experiments are also presented to illustrate the analysis.