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  • 1
    Electronic Resource
    Electronic Resource
    Legendre and Chebyshev spectral approximations of Burgers' equation (1981)
    Springer
    Numerische Mathematik 37 (1981), S. 321-332 
    Details
    ISSN: 0945-3245
    Keywords: (1980). AMS (MOS) ; Primary 41A10 ; Secondary 65N15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We give error estimates for both Legendre and Chebyshev spectral approximations of the steady state Burgers' problem $$ - u_{xx} + \lambda (uu_x - f) = 0 in I = ( - 1,1); u( - 1) = u(1) = 0. $$ To do that we prove some abstract approximation properties of orthogonal projection operators in some weighted Sobolev spacesH ω s (I) for both Legendre and Chebyshev weights.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400311
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  • 2
    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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  • 3
    Electronic Resource
    Electronic Resource
    Combined finite element and spectral approximation of the Navier-Stokes equations (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 201-217 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Resumé On présente une méthode d'approximation numérique des équations de Navier-Stokes possédant une direction de périodicité. Dans cette direction une méthode pseudospectrale basée sur des développements en série de Fourier est utilisée, dans les deux autres on applique une méthode d'éléments finis standard. On montre que la convergence est optimale et que les deux paramètres de discrétisation peuvent être choisis de façon indépendante.
    Notes: Summary We present a method for the numerical approximation of Navier-Stokes equations with one direction of periodicity. In this direction a Fourier pseudospectral method is used, in the two others a standard F.E.M. is applied. We prove optimal rate of convergence where the two parameters of discretization intervene independently.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01410105
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  • 4
    Electronic Resource
    Electronic Resource
    Analysis of a part design procedure (1995)
    Springer
    Numerische Mathematik 71 (1995), S. 465-510 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):49Q10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. In this paper we analyze and illustrate a new "ab initio" part design procedure, in which, given a cost function which reflects performance, materials, and manufacturing considerations, the topology and the geometry of the part are automatically produced. The analysis is based on demonstration of, first, the compactness of the metric space over which the cost function is defined, and, second, lower semi-continuity of the cost function. Examples include beams and elastic supports.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050154
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  • 5
    Electronic Resource
    Electronic Resource
    Scalar and vector potentials' coupling on nonmatching grids for the simulation of an electromagnetic brake (2005)
    Bradford : Emerald
    Compel 24 (2005), S. 1061-1070 
    Details
    ISSN: 0332-1649
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Purpose - We present a method for the simulation of the dynamical behavior of a coupled magneto-mechanical system given in terms of a conductor moving through an electromagnetic field. Design/methodology/approach - For the magnetic part, we consider a model based on an electric vector and a magnetic scalar potential, whereas the mechanical part is modelled by the equation of a rigid body motion. A weak coupling is employed: at each time step the resulting forces are calculated yielding the new displacement of the conductor. Findings - Numerical results are given for the simulation of an electromagnetic brake with axisymmetric geometry. They indicate that the proposed method is especially well suited for eddy current problems involving moving conductors. Research limitations/implications - Further research should be undertaken toward the application of the proposed method to real 3D problems. Originality/value - The spatial discretization of the problem relies on the use of two independent triangulations to approximate the two involved potentials. Whereas the scalar magnetic potential is discretized by means of nodal H1-conforming finite elements on a grid covering the global computational domain, the vector electric potential is approximated by Hcurl-conforming edge elements on another grid only covering the conductor. The coupling between the two grids is accomplished via the mortar finite element method. At each time step, only the coupling matrix has to be reassembled, all other involved matrices remain the same. Moreover, no remeshing is necessary when the conductor changes its position. The paper should be valuable for any researcher interested in the numerical simulation of eddy current problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/03321640510571246
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Spectral element multigrid. II. Theoretical justification (1988)
    Springer
    Journal of scientific computing 3 (1988), S. 323-353 
    Details
    ISSN: 1573-7691
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We analyze here a multigrid algorithm used for solving iteratively the algebraic system resulting from the approximation of a second-order problem by spectral or spectral element methods. The analysis, performed here in the one-dimensional case, justifies the good smoothing properties of the Jacobi preconditioner that has been presented in Part I of this paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01065177
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  • 7
    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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