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Stabilizing the Hierarchical Basis by Approximate Wavelets, I: Theory
Author(s) -
Vassilevski Panayot S.,
Wang Junping
Publication year - 1997
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/(sici)1099-1506(199703/04)4:2<103::aid-nla101>3.0.co;2-j
Subject(s) - mathematics , preconditioner , basis (linear algebra) , multiplicative function , wavelet , basis function , finite element method , action (physics) , order (exchange) , algorithm , mathematical analysis , computer science , geometry , iterative method , physics , finance , quantum mechanics , artificial intelligence , economics , thermodynamics
This paper proposes a stabilization of the classical hierarchical basis (HB) method by modifying the HB functions using some computationally feasible approximate L 2 ‐projections onto finite element spaces of relatively coarse levels. The corresponding multilevel additive and multiplicative algorithms give spectrally equivalent preconditioners, and one action of such a preconditioner is of optimal order computationally. The results are regularity‐free for the continuous problem (second order elliptic) and can be applied to problems with rough coefficients and local refinement. © 1997 by John Wiley & Sons, Ltd.