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.
Author: | Folkmar A. Bornemann, Harry Yserentant |
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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 |