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Multilevel Preconditioners for Mixed Methods for Second Order Elliptic Problems
Author(s) -
Chen Zhangxin,
Ewing Richard E.,
Lazarov Raytcho D.,
Maliassov Serguei,
Kuznetsov Yuri A.
Publication year - 1996
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(199609/10)3:5<427::aid-nla92>3.0.co;2-i
Subject(s) - mathematics , finite element method , tetrahedron , triangulation , lagrange multiplier , algebraic number , linear system , mixed finite element method , simple (philosophy) , algebra over a field , mathematical analysis , pure mathematics , mathematical optimization , geometry , philosophy , physics , epistemology , thermodynamics
A new approach for constructing algebraic multilevel preconditioners for mixed finite element methods for second order elliptic problems with tensor coefficients on general geometry is proposed. The linear system arising from the mixed methods is first algebraically condensed to a symmetric, positive definite system for Lagrange multipliers, which corresponds to a linear system generated by standard nonconforming finite element methods. Algebraic multilevel preconditioners for this system are then constructed based on a triangulation of the domain into tetrahedral substructures. Explicit estimates of condition numbers and simple computational schemes are established for the constructed preconditioners. Finally, numerical results for the mixed finite element methods are presented to illustrate the present theory.