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  <doc>
    <id>71</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1992-02-03</completedDate>
    <publishedDate>1992-02-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Basic Norm Equivalence for the Theory of Multilevel Methods.</title>
    <abstract language="eng">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.</abstract>
    <identifier type="serial">SC-92-01</identifier>
    <identifier type="opus3-id">70</identifier>
    <identifier type="doi">10.1007/BF01388699</identifier>
    <note>No preprint available</note>
    <enrichment key="SourceTitle">Appeared in: Numer. Math. 64 (1993) pp. 455-476</enrichment>
    <author>Folkmar A. Bornemann</author>
    <author>Harry Yserentant</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-92-01</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>multilevel methods</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonuniform meshes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal convergence rates</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="65N30">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="msc" number="65N50">Mesh generation and refinement</collection>
    <collection role="msc" number="65N55">Multigrid methods; domain decomposition</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
  </doc>
</export-example>
