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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Computing 49 (1992), S. 11-23 
    ISSN: 1436-5057
    Keywords: 65M55 ; 65Y05 (primary) ; 65M60 (secondary) ; Domain decomposition ; parallel time stepping ; parabolic problems ; transputer system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Implementierung von Lösungs-methoden für parabolische Probleme erfordert eine ausreichende Balance zwischen der parallelen Effizienz voll-expliziter Schemata und der Notwendigkeit von Stabilität und Genauigkeit, welche einen gewissen Grad an Implizitheit bedingt. Als ein Kompromiß wird ein Gebietszerlegungsverfahren vorgeschlagen, welches lokal implizit ist auf leicht überlappenden Teilgebieten, die lokalen Randdaten aber durch einen einfachen expliziten Prozeß fortpflanzt. Die Analyse dieses Algorithmus zeigt, daß er zufriedenstellende Stabilitäts- und Approximationseigenschaften besitzt und effektiv parallelisiert werden kann. Diese theoretischen Resultate werden bestätigt durch numerische Tests auf einem Transputer-System.
    Notes: Abstract In the parallel implementation of solution methods for parabolic problems one has to find a proper balance between the parallel efficiency of a fully explicit scheme and the need for stability and accuracy which requires some degree of implicitness. As a compromise a domain splitting scheme is proposed which is locally implicit on slightly overlapping subdomains but propagates the corresponding boundary data by a simple explicit process. The analysis of this algorithm shows that it has satisfactory stability and approximation properties and can be effectively parallelized. These theoretical results are confirmed by numerical tests on a transputer system.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Computational mechanics 6 (1990), S. 221-236 
    ISSN: 1432-0924
    Keywords: 65 N 30 ; 73 K 10 ; 73 K 25
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Most of the existing convergence theory of mixed finite element methods for solving the plate bending problem converns the model case of a purely clamped or simply supported plate with sufficiently regular boundary. The extension of this analysis to more complicated situations encounters two major difficulties: first, the problem of verifying the stability of the schemes in the case of a partially free boundary and, second, the reduction of the solution's regularity in the presence of reentrant corners or changes in the type of the boundary conditions. In this paper these questions are studied for the approximation of the Kirchhoff plate model by one of the mixed finite element schemes due to L. R. Herrmann, the so-called “first Herrmann scheme”. It is shown that this method converges on any polygonal domain and for all usual boundary conditions. The proof is based on the fact that this particular mixed scheme is algebraically equivalent to a nonconforming displacement method.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 8 (1992), S. 97-111 
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A simple nonconforming quadrilateral Stokes element based on “rotated” multi-linear shape functions is analyzed. On strongly nonuniform meshes the usual parametric version of this element suffers from a lack of consistency, while its nonparametric counterpart turns out to be convergent with optimal orders. This theoretical result is confirmed by numerical tests.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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