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  • 1
    Digitale Medien
    Digitale Medien
    Convergence of finite-difference techniques for a harmonic mixed boundary value problem (1970)
    Springer
    BIT 10 (1970), S. 366-374 
    Details
    ISSN: 1572-9125
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The paper deals with the convergence of finite-difference approximations for a harmonic mixed boundary value problem. In particular the case when the boundary contains a slit is considered.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01934205
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  • 2
    Digitale Medien
    Digitale Medien
    Cubic spline interpolation of harmonic functions (1974)
    Springer
    BIT 14 (1974), S. 452-459 
    Details
    ISSN: 1572-9125
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract It is shown that for the two dimensional Laplace equation a univariate cubic spline approximation in either space direction together with a difference approximation in the other leads to the well-known nine-point finite-difference formula. For harmonic problems defined in rectangular regions this property provides a means of determining with ease accurate approximations at any point in the region.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01932541
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  • 3
    Digitale Medien
    Digitale Medien
    Towards adaptive finite element schemes for partial differential Volterra equation solvers (1996)
    Springer
    Advances in computational mathematics 6 (1996), S. 309-323 
    Details
    ISSN: 1572-9044
    Schlagwort(e): finite element method ; discontinuous Galerkin method ; a posteriori error estimates ; adaptivity ; Volterra equations ; viscoelasticity ; 45K05
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We give a brief indication of how elliptic, parabolic and hyperbolic partial differential equations with memory arise when modelling viscoelastic materials. We then point out the urgent need for adaptive solvers for these problems and, employing the methodology of Eriksson, Johnson et al. (e.g., SIAM J. Numer. Anal. 28 (1991)), we given ana posteriori error estimate for a model two-point hereditary boundary value problem. The strengths and weaknesses of the analysis and estimate are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02127710
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  • 4
    Digitale Medien
    Digitale Medien
    Treatment of harmonic mixed boundary problems by conformal transformation methods (1972)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 23 (1972), S. 655-664 
    Details
    ISSN: 1420-9039
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Beschreibung / Inhaltsverzeichnis: Résumé On propose ici une méthode qui se compose de trois transformations conformes pour la solution numérique d'une classe de problèmes harmoniques aux valeurs frontières mixtes qui comprend des singularités. Quoique cette méthode soit moins versatile que les méthodes bien connues des différences et des éléments finis, on trouve qu'elle convient mieux aux problèmes de ce genre. Les descriptions des transformations sont présentées en détail dans cet article et les mérites et désavantages en sont débattus objectivement.
    Notizen: Summary A method consisting of three conformal transformations is used for the numerical solution of a class of harmonic mixed boundary value problems containing boundary singularities. The method, although less flexible than the well-known finite-difference and finite element techniques, is very well suited to problems of this class. In the present paper the transformations are described in detail and the merits and shortcomings of the method are discussed objectively.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01593987
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  • 5
    Digitale Medien
    Digitale Medien
    Error bounds for finite element solutions of mildly nonlinear elliptic boundary value problems (1976)
    Springer
    Numerische Mathematik 26 (1976), S. 107-116 
    Details
    ISSN: 0945-3245
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary The equivalence in a Hilbert space of variational and weak formulations of linear elliptic boundary value problems is well known. This same equivalence is proved here for mildly nonlinear problems where the right hand side of the differential equation involves the solution function. A finite element approximation to the solution of the weak problem ina finite dimensional subspace of the original Hilbert space is defined. An inequality bounding the error in this approximation over all functions of the space is derived, and in particular this holds for an interpolant to the weak solution. Thus this inequality, together with previously known, interpolation error bounds, produces a bound on the finite element solution to this nonlinear problem. An example of a mildly nonlinear Poisson problem is given.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01396570
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  • 6
    Digitale Medien
    Digitale Medien
    A numerical conformal transformation method for harmonic mixed boundary value problems in polygonal domains (1973)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 24 (1973), S. 304-316 
    Details
    ISSN: 1420-9039
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Beschreibung / Inhaltsverzeichnis: Résumé Une méthode est décrite ici pour la solution numérique d'une classe de problèmes mixtes harmoniques aux valeurs aux limites dans des domaines simplement connexes. La méthode consiste en trois transformations conformes consécutives dont la première doit être accomplie numériauement. La méthode est plus particulièrement appliquée aux problèmes définis dans des domaines polygonaux possédant des angles rentrants où apparaissent des singularités.
    Notizen: Summary A method is described for the numerical solution of harmonic mixed boundary value problems in simply-connected domains. The method consists of three successive conformal transformations of which the first is performed numerically. In particular the method is applied to problems, defined in polygonal regions, containing re-entrant cornes at which boundary singularities occur.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01595198
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  • 7
    Digitale Medien
    Digitale Medien
    Finite difference solution of a system of first-order partial differential equations (1981)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 1385-1395 
    Details
    ISSN: 0029-5981
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: A finite difference solution of a system of first-order partial differential equations, using a central difference scheme, is presented. The equations describe the linear elastic behaviour of a thick rectangular plate resting on an elastic foundation and carrying an arbitrary transverse load. The lateral edges of the plate are unstressed. The main deflections and stresses predicted by the method for a particular case are given, together for purposes of comparison, with results from a finite element analysis.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nme.1620170907
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  • 8
    Digitale Medien
    Digitale Medien
    Fourier series solution for a rectangular thick plate with free edges on an elastic foundation (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1801-1820 
    Details
    ISSN: 0029-5981
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: A Fourier series solution is presented for a system of first-order partial differential equations which describe the linear elastic behaviour of a thick rectangular plate resting on an elastic foundation and carrying an arbitrary transverse load. The lateral edges of the plate are unstressed. A central step in the method for solving the system of equations is to combine a complementary function with a particular solution of the system in order to satisfy the boundary conditions. The complementary function is the sum of two series. The terms of the first series are products of a Fourier term in one space variable with the solution of an eigenvalue problem in the other space variable. The second series is similar and comes from reversing the roles of the space variables.
    Zusätzliches Material: 9 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nme.1620181205
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  • 9
    Digitale Medien
    Digitale Medien
    Numerical Analysis, Roger Temam. D. Reidel Publishing Company, Dordrcht, 1973 (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 733-733 
    Details
    ISSN: 0029-5981
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nme.1620090323
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  • 10
    Digitale Medien
    Digitale Medien
    General conical singularities in three-dimensional Poisson problems (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 215-235 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Zusätzliches Material: 14 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670110204
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