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2008•SIAM Journal on Numerical AnalysisRequires access

A Laguerre–Legendre Spectral Method for the Stokes Problem in a Semi-Infinite Channel

Mejdi Azaïez, Jie Shen, Chuanju Xu, Qingqu Zhuang

Open publisher page 19 citations

Abstract

A mixed spectral method is proposed and analyzed for the Stokes problem in a semi-infinite channel. The method is based on a generalized Galerkin approximation with Laguerre functions in the x direction and Legendre polynomials in the y direction. The well-posedness of this method is established by deriving a lower bound on the inf-sup constant. Numerical results indicate that the derived lower bound is sharp. Rigorous error analysis is also carried out.

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What this paper is about

A mixed spectral method is proposed and analyzed for the Stokes problem in a semi-infinite channel. The method is based on a generalized Galerkin approximation with Laguerre functions in the x direction and Legendre polynomials in the y direction. The well-posedness of this method is established by deriving a lower bound on the inf-sup constant. Numerical results indicate that the derived lower bound is sharp. Rigorous error analysis is also carried out.

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Available abstract

A mixed spectral method is proposed and analyzed for the Stokes problem in a semi-infinite channel. The method is based on a generalized Galerkin approximation with Laguerre functions in the x direction and Legendre polynomials in the y direction. The well-posedness of this method is established by deriving a lower bound on the inf-sup constant. Numerical results indicate that the derived lower bound is sharp. Rigorous error analysis is also carried out.

Key concepts: Laguerre polynomials, Legendre polynomials, Mathematics, Galerkin method, Mathematical analysis, Laguerre's method, Spectral method, Associated Legendre polynomials

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