• Corpus ID: 221396898

Multilevel decompositions and norms for negative order Sobolev spaces

  title={Multilevel decompositions and norms for negative order Sobolev spaces},
  author={Thomas Fuhrer},
We consider multilevel decompositions of piecewise constants on simplicial meshes that are stable in H−s for s ∈ (0, 1). Proofs are given in the case of uniformly and locally refined meshes. Our findings can be applied to define local multilevel diagonal preconditioners that lead to bounded condition numbers (independent of the mesh-sizes and levels) and have optimal computational complexity. Furthermore, we discuss multilevel norms based on local (quasi-)projection operators that allow the… 
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