TY - GEN A1 - Bornemann, Folkmar A. A1 - Yserentant, Harry T1 - A Basic Norm Equivalence for the Theory of Multilevel Methods. N2 - 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. T3 - ZIB-Report - SC-92-01 KW - multilevel methods KW - nonuniform meshes KW - optimal convergence rates Y1 - 1992 U6 - https://doi.org/10.1007/BF01388699 N1 - No preprint available ER -