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

• Published in: Applied numerical mathematics Vol. 120; pp. 35 - 52
• Main Authors: Hessari, Peyman, Shin, Byeong-Chun
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2017
• Subjects: Beavers–Joseph–Saffman interface conditions; Coupled Stokes–Darcy equations; First order system least squares method; Legendre and Chebyshev spectral approximation; Coupled Stokes–Darcy equations; Beavers–Joseph–Saffman interface conditions; Legendre and Chebyshev spectral approximation; First order system least squares method
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/j.apnum.2017.04.010

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.