Volume 45, pp. 160-182, 2016.

Least squares spectral method for velocity-flux form of the coupled Stokes-Darcy equations

Peyman Hessari and Bongsoo Jang

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 $H^1$ and $H(\mathrm{d}\mathrm{i}\mathrm{v})$-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.

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Key words

Coupled Stokes-Darcy equation, first order system, least squares method, Legendre and Chebyshev pseudo-spectral method, Beavers-Joseph-Saffman law.

AMS subject classifications

65N35, 65N12.