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Robust optimal multilevel preconditioners for non‐conforming finite element systems
Author(s) -
Blaheta R.,
Margenov S.,
Neytcheva M.
Publication year - 2005
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.438
Subject(s) - mathematics , robustness (evolution) , discretization , multiplicative function , finite element method , linear algebra , linear system , algebraic number , mathematical optimization , algebra over a field , pure mathematics , mathematical analysis , geometry , biochemistry , chemistry , physics , gene , thermodynamics
We consider strategies to construct optimal order two‐ and multilevel hierarchical preconditioners for linear systems as arising from the finite element discretization of self‐adjoint second order elliptic problems using non‐conforming Crouzeix–Raviart linear elements. In this paper we utilize the hierarchical decompositions, derived in a previous work by the same authors ( Numerical Linear Algebra with Applications 2004; 11 :309–326) and provide a further analysis of these decompositions in order to assure robustness with respect to anisotropy. Finally, we show how to construct both multiplicative and additive versions of the algebraic multilevel iteration preconditioners and show robustness and optimal order convergence estimates. Copyright © 2005 John Wiley & Sons, Ltd.