A Coupled Legendre-Laguerre Spectral-Element Method for the Navier-Stokes Equations in Unbounded Domains

  • Qingqu Zhuang
  • Jie Shen
  • Chuanju Xu


A coupled Legendre-Laguerre spectral element method is proposed for the Stokes and Navier-Stokes equations in unbounded domains. The method combines advantages of the high accuracy of the Laguerre-spectral method for unbounded domains and the geometric flexibility of the spectral-element method. Rigorous stability and error analysis for the Stokes problem is carried out. Numerical results indicate that the proposed method is very effective for some realistic flow problems in unbounded domains, such as flows passing a circular cylinder.


Laguerre functions Legendre polynomials Navier-Stokes equations Stokes equations Inf-sup condition Error analysis Spectral element Computational fluid dynamics 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.School of Mathematical SciencesXiamen UniversityXiamenChina
  2. 2.Department of MathematicsPurdue UniversityWest LafayetteUSA

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