A basic norm equivalence for the theory of multilevel methods

Folkmar Bornemann, Harry Yserentant

Research output: Contribution to journalArticlepeer-review

69 Scopus citations


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 have proved the equivalence of the associated discrete norms with the H1-norm. The present paper 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.

Original languageEnglish
Pages (from-to)455-476
Number of pages22
JournalNumerische Mathematik
Issue number1
StatePublished - Dec 1993
Externally publishedYes


  • Mathematics Subject Classification (1991): 65N55, 65N50


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