A basic norm equivalence for the theory of multilevel methods

Summary Subspace decompositions of finite element spaces based onL ₂-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 theH ¹-norm. The present paper gives an elementary, self-contained derivation of this result which is based on the use ofK-functionals known from the theory of interpolation spaces.