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  • 1
    Electronic Resource
    Electronic Resource
    An accurate semi-analytic finite difference scheme for two-dimensional elliptic problems with singularities (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 281-296 
    Details
    ISSN: 0749-159X
    Keywords: singularities ; elliptic PDE ; Laplace equation ; high-order Finite Difference Schemes ; Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A high-order semi-analytic finite difference scheme is presented to overcome degradation of numerical performance when applied to two-dimensional elliptic problems containing singular points. The scheme, called Least-Square Singular Finite Difference Scheme (L-S SFDS), applies an explicit functional representation of the exact solution in the vicinity of the singularities, and a conventional finite difference scheme on the remaining domain. It is shown that the L-S SFDS is “pollution” free, i.e., no degradation in the convergence rate occurs because of the singularities, and the coefficients of the asymptotic solution in the vicinity of the singularities are computed as a by-product with a very high accuracy. Numerical examples for the Laplace and Poisson equations over domains containing re-entrant corners or abrupt changes in the boundary conditions are presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 281-296, 1998
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
  • 2
    Electronic Resource
    Electronic Resource
    HIGH-ORDER-ACCURATE DISCRETIZATION STENCIL FOR AN ELLIPTIC EQUATION (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 367-377 
    Details
    ISSN: 0271-2091
    Keywords: discretization ; high-order accuracy ; duct flow ; 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: The coefficients for a nine-point high-order-accurate discretization scheme for an elliptic equation ∇2u- γ2u=r0 (∇2 is the two-dimensional Laplacian operator) are derived. Examples with Dirichlet and Neumann boundary condtions are considered. In order to demonstrate the high-order accuracy of the method, numerical results are compared with exact solutions.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
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