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A Basic Norm Equivalence for the Theory of Multilevel Methods.

  • 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.

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Metadaten
Author:Folkmar A. Bornemann, Harry Yserentant
Document Type:ZIB-Report
Tag:multilevel methods; nonuniform meshes; optimal convergence rates
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N50 Mesh generation and refinement
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N55 Multigrid methods; domain decomposition
Date of first Publication:1992/02/03
Series (Serial Number):ZIB-Report (SC-92-01)
ZIB-Reportnumber:SC-92-01
Notes:
No preprint available
Published in:Appeared in: Numer. Math. 64 (1993) pp. 455-476
DOI:https://doi.org/10.1007/BF01388699
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