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Two Preconditioners Based on the Multi-Level Splitting of Finite Element Spaces.

Please always quote using this URN: urn:nbn:de:0297-zib-274
  • 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; our theory is based exclusively on local properties like the shape regularity of the finite elements.

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Metadaten
Author:Harry Yserentant
Document Type:ZIB-Report
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F10 Iterative methods for linear systems [See also 65N22]
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F35 Matrix norms, conditioning, scaling [See also 15A12, 15A60]
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N20 Ill-posed problems
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Date of first Publication:1989/11/17
Series (Serial Number):ZIB-Report (SC-89-09)
ZIB-Reportnumber:SC-89-09
Published in:Appeared in: Numer. Math. 58 (1990), pp. 163-184
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