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  • 1990-1994  (4)
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Material
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Year
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  • 1
    Electronic Resource
    Electronic Resource
    A basic norm equivalence for the theory of multilevel methods (1993)
    Springer
    Numerische Mathematik 64 (1993), S. 455-476 
    Details
    ISSN: 0945-3245
    Keywords: 65N55 ; 65N50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Subspace decompositions of finite element spaces based onL 2-like orthogonal projections play an important role for the construction and analysis of multigrid like iterative methods. Recently several authors have proved the equivalence of the associated discrete norms with theH 1-norm. The present paper gives an elementary, self-contained derivation of this result which is based on the use ofK-functionals known from the theory of interpolation spaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01388699
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Two preconditioners based on the multi-level splitting of finite element spaces (1990)
    Springer
    Numerische Mathematik 58 (1990), S. 163-184 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65F10 ; 65F35 ; 65N20 ; 65N30 ; CR: G 1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The hierarchical basis preconditioner and the recent preconditioner of Bramble, Pasciak and Xu are derived and analyzed within a joint framework. This discussion elucidates the close relationship between both methods. Special care is devoted to highly nonuniform meshes; exclusively local properties like the shape regularity of the finite elements are utilized.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385617
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    Paper (German National Licenses)
    Fulltext
  • 3
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    Unknown
    A Basic Norm Equivalence for the Theory of Multilevel Methods. (1992)
    Details
    Publication Date: 2014-02-26
    Description: Subspace decompositions of finite element spaces based on $L2$-like orthogonal projections play an important role for the construction and analysis of multigrid like iterative methods. Recently several authors proved the equivalence of the associated discrete norms with the $H^1$-norm. The present report gives an elementary, self-contained derivation of this result which is based on the use of $ K$-functionals known from the theory of interpolation spaces. {\bf Keywords:} multilevel methods, nonuniform meshes, optimal convergence rates. {\bf AMS(MOS) Subject classifications:} 65N55, 65N30, 65N50.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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    OPUS
  • 4
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    Multilevel Methods for Elliptic Problems on Domains not Resolved by the Coarse Grid. (1993)
    Details
    Publication Date: 2014-02-26
    Description: Elliptic boundary value problems are frequently posed on complicated domains which cannot be covered by a simple coarse initial grid as it is needed for multigrid like iterative methods. In the present article, this problem is resolved for selfadjoint second order problems and Dirichlet boundary conditions. The idea is to construct appropriate subspace decompositions of the corresponding finite element spaces by way of an embedding of the domain under consideration into a simpler domain like a square or a cube. Then the general theory of subspace correction methods can be applied.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
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    OPUS
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