Two preconditioners based on the multi-level splitting of finite element spaces
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- Yserentant, H. Numer. Math. (1990) 58: 163. doi:10.1007/BF01385617
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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.