Geodesic
Least squares spectral method for velocity-flux form of the coupled Stokes-Darcy equations
Electronic transactions on numerical analysis, Tome 45 (2016), pp. 160-182
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.
Classification : 65N35, 65N12
Keywords: coupled Stokes-Darcy equation, first order system, least squares method, Legendre and Chebyshev pseudo-spectral method, Beavers-Joseph-Saffman law 
@article{ETNA_2016__45__a17,
     author = {Hessari,  Peyman and Jang,  Bongsoo},
     title = {Least squares spectral method for velocity-flux form of the coupled {Stokes-Darcy} equations},
     journal = {Electronic transactions on numerical analysis},
     pages = {160--182},
     year = {2016},
     volume = {45},
     zbl = {1338.65255},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2016__45__a17/}
}
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%A Jang,  Bongsoo
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%F ETNA_2016__45__a17
Hessari,  Peyman; Jang,  Bongsoo. Least squares spectral method for velocity-flux form of the coupled Stokes-Darcy equations. Electronic transactions on numerical analysis, Tome 45 (2016), pp. 160-182. http://geodesic.mathdoc.fr/item/ETNA_2016__45__a17/