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  • 1
    Electronic Resource
    Electronic Resource
    Spectral approximation of the periodic-nonperiodic Navier-Stokes equations (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 655-700 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30: 65N35 ; CR:G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In order to approximate the Navier-Stokes equations with periodic boundary conditions in two directions and a no-slip boundary condition in the third direction by spectral methods, we justify by theoretical arguments an appropriate choice of discrete spaces for the velocity and the pressure. The compatibility between these two spaces is checked via an infsup condition. We analyze a spectral and a collocation pseudo-spectral method for the Stokes problem and a collocation pseudo-spectral method for the Navier-Stokes equations. We derive error bounds of spectral type, i.e. which behave likeM −σ whereM depends on the number of degrees of freedom of the method and σ represents the regularity of the data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400175
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Méthodes spectrales dans une portion de disque (1996)
    Springer
    Numerische Mathematik 73 (1996), S. 265-289 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Summary. This paper is devoted to spectral methods for the discretization of elliptic equations in a part of a disk, relying on the use of polar coordinates and approximation by high degree polynomials with respect to each coordinate. We describe the discretization for two model problems: the Poisson equation and the bilaplacian equation, we perform the numerical analysis in each case and we present numerical results.
    Notes: Résumé. On propose une méthode spectrale pour la discrétisation d'équations elliptiques dans une portion de disque, par passage en coordonnées polaires et approximation par des polynômes de degréélevé par rapport à chaque coordonnée. On décrit la discrétisation pour deux problèmes modèle: l'équation de Poisson et l'équation du bilaplacien, on en effectue l'analyse et on présente des résultats numériques.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050193
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A collocation method over staggered grids for the Stokes problem (1988)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 537-557 
    Details
    ISSN: 0271-2091
    Keywords: Spectral methods ; Stokes problem ; Collocation ; Staggered grids ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper is devoted to the description and the detailed numerical analysis of a new spectral collocation method for the Stokes problem in a square, involving three staggered grids.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650080504
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    Paper (German National Licenses)
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