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  • 65N30  (3)
  • 35Q72  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    The Wiener-Hopf method for systems of pseudodifferential equations with an application to crack problems (1995)
    Springer
    Integral equations and operator theory 23 (1995), S. 294-335 
    Details
    ISSN: 1420-8989
    Keywords: 35Q72 ; 35D10 ; 45E10 ; 47B35 ; 47G30 ; 41A60
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The aim of this paper is to develop the Wiener-Hopf method for systems of pseudo-differential equations with “non-constant coefficients” and to apply it to the describtion of the asymptotic behaviour of solutions to boundary integral equations for crack problems when a crack occurs in a linear anisotropic elastic medium. The method was suggested in [15] for scalar pseudo-differential equations with “constant coefficients” and applied in [7] to the crack problems in the isotropic case. The existence and a-priori smoothness of solutions for the anisotropic case has been proved in [11, 12], while the isotropic case has been treated earlier in [7, 25, 41, 50]. Our results improve even those for the isotropic case obtained in [7, 50]. Asymptotic estimates for the behaviour of solutions in the anisotropic case have been obtained in [28] by a different method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01198487
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  • 2
    Electronic Resource
    Electronic Resource
    Adaptive boundary element methods for strongly elliptic integral equations (1988)
    Springer
    Numerische Mathematik 53 (1988), S. 539-558 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65N45 ; 65R20 ; 65N99 ; 65N30 ; 65D07 ; 45J05 ; 45B05 ; 45E05 ; 45L10 ; R: 61.9
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Integral operators are nonlocal operators. The operators defined in boundary integral equations to elliptic boundary value problems, however, are pseudo-differential operators on the boundary and, therefore, provide additional pseudolocal properties. These allow the successful application of adaptive procedures to some boundary element methods. In this paper we analyze these methods for general strongly elliptic integral equations and obtain a-posteriori error estimates for boundary element solutions. We also apply these methods to nodal collocation with odd degree splines. Some numerical examples show that these adaptive procedures are reliable and effective.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397551
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  • 3
    Electronic Resource
    Electronic Resource
    Galerkin collocation for an improved boundary element method for a plane mixed boundary value problem (1984)
    Springer
    Computing 33 (1984), S. 269-296 
    Details
    ISSN: 1436-5057
    Keywords: 65R20 ; 65N30 ; 45L10 ; 35J05 ; Boundary element method ; singular elements ; error estimates including numerical quadrature
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir beschreiben die numerische Durchführung einer Randelement-Approximation für das ebene gemischte Randwertproblem für harmonische Funktionen. Grundlage unseres Galerkin-Verfahrens ist die direkte Randintegralmethode. Die Genauigkeit des Verfahrens wird dadurch verbessert, daß neben quadratischen Splines geeignete Singularitätenfunktionen als zusätzliche Test- und Ansatzfunktionen verwendet werden. Wir analysieren die Konsistenz der verwendeten numerischen Integrationen und erhalten asymptotische Fehlerabschätzungen der voll diskretisierten Näherungsgleichungen. Diese sind von den gleichen optimalen Ordnungen wie die entsprechenden Galerkin-Fehler.
    Notes: Abstract We present the numerical implementation of a boundary element approximation for the plane mixed boundary value problem of the Laplacian. The performed Galerkin procedure is based on the direct boundary integral method. Its accuracy is improved by using appropriate singularity functions as additional test and trial functions besides quadratic splines. We analize the consistency error of the used numerical integrations and present asymptotic error estimates for the fully discretized numerical scheme which are of the same optimal orders as the Galerkin errors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02242273
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  • 4
    Electronic Resource
    Electronic Resource
    The fast Fourier transform and the numerical solution of one-dimensional boundary integral equations (1985)
    Springer
    Numerische Mathematik 47 (1985), S. 15-38 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65E05 ; 65N45 ; 45L05 ; 45L10 ; 65R99 ; 65N30 ; 65J10 ; 65R20 ; 47G05 ; 45J05 ; 45F15 ; 47B35 ; CR: G1.9
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Here we present a fully discretized projection method with Fourier series which is based on a modification of the fast Fourier transform. The method is applied to systems of integro-differential equations with the Cauchy kernel, boundary integral equations from the boundary element method and, more generally, to certain elliptic pseudodifferential equations on closed smooth curves. We use Gaussian quadratures on families of equidistant partitions combined with the fast Fourier transform. This yields an extremely accurate and fast numerical scheme. We present complete asymptotic error estimates including the quadrature errors. These are quasioptimal and of exponential order for analytic data. Numerical experiments for a scattering problem, the clamped plate and plane estatostatics confirm the theoretical convergence rates and show high accuracy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389873
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