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A Basic Norm Equivalence for the Theory of Multilevel Methods. (1992)

Bornemann, Folkmar A. ; Yserentant, Harry

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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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