## 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 $H(\rm {div})$-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.

Full Text (PDF) [351 KB]

### Key words

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

65N35, 65N12.

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