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  • 65F10  (1)
  • 65N30  (1)
  • 65N50  (1)
  • 65Y99  (1)
  • Data structures  (1)
  • ddc:000  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Computing 55 (1995), S. 325-354 
    ISSN: 1436-5057
    Keywords: 65N50 ; 65Y99 ; 65N30 ; 65N55 ; 65F10 ; Data structures ; adaptive finite element methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Für die Verwaltung von extrem nichtuniformen, adaptiv erzeugten Finite element Gittern benötigt man spezielle Techniken und Datenstrukturen. Eine Datenstruktur dieser Art wird in diesem Artikel beschrieben. Basisstrukturen sind Punkte, Kanten und Dreiecke. Die Datenstruktur ist besonders zugeschnitten auf iterative Löser wie die hierarchische Basis oder die “multilevel nodal basis” Methode.
    Notes: Abstract The administration of strongly nonuniform, adaptively generated finite element meshes requires specialized techniques and data structures. A special data structure of this kind is described in this paper. It relies on points, edges and triangles as basic structures and is especially well suited for the realization of iterative solvers like the hierarchical basis or the multilevel nodal basis method.
    Type of Medium: Electronic Resource
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  • 2
    Publication Date: 2014-02-26
    Description: The paper presents the mathematical concepts underlying the new adaptive finite element code KASKADE, which, in its present form, applies to linear scalar second-order 2-D elliptic problems on general domains. Starting point for the new development is the recent work on hierarchical finite element bases due to Yserentant (1986). It is shown that this approach permits a flexible balance between iterative solver, local error estimator, and local mesh refinement device - which are the main components of an adaptive PDE code. Without use of standard multigrid techniques, the same kind of computational complexity is achieved - independent of any uniformity restrictions on the applied meshes. In addition, the method is extremely simple and all computations are purely local - making the method particularly attractive in view of parallel computing. The algorithmic approach is illustrated by a well-known critical test problem. {\bf Keywords:} finite elements, hierarchical basis, adaptive mesh refinement, preconditioned conjugate gradient methods.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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