Summary
The hierarchical basis preconditioner and the recent preconditioner of Bramble, Pasciak and Xu are derived and analyzed within a joint framework. This discussion elucidates the close relationship between both methods. Special care is devoted to highly nonuniform meshes; exclusively local properties like the shape regularity of the finite elements are utilized.
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The author was supported by the Konrad-Zuse-Zentrum für Informationstechnik Berlin, Federal Republic of Germany
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Yserentant, H. Two preconditioners based on the multi-level splitting of finite element spaces. Numer. Math. 58, 163–184 (1990). https://doi.org/10.1007/BF01385617
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DOI: https://doi.org/10.1007/BF01385617