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Short Communication: A note on optimal hybrid V ‐cycle multilevel algorithms for mixed finite element systems with penalty term
Author(s) -
Lai ChenYao G.
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(199711/12)4:6<491::aid-nla116>3.0.co;2-k
Subject(s) - finite element method , mathematics , algorithm , term (time) , element (criminal law) , decomposition , penalty method , boundary value problem , boundary (topology) , mathematical optimization , mathematical analysis , engineering , ecology , physics , quantum mechanics , political science , law , biology , structural engineering
In this paper, we investigate some cost‐effective hybrid V ‐cycle multilevel algorithms for the discrete systems that arise when a mixed finite element approach is used to solve certain second‐order elliptic boundary value problems. By introducing a small penalty parameter, the perturbed indefinite system can be reduced to a symmetric positive definite system involving the unknown flux alone. We study the numerical behaviour of some hybrid V ‐cycle multilevel algorithms with optimal computational complexity based on the hierarchical spatial decomposition approach proposed by Cai, Goldstein and Pasciaks for the reduced system. © 1997 by John Wiley & Sons, Ltd.