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Finite element methods for elliptic systems with constraints
Author(s) -
Dobrowolski Manfred
Publication year - 1999
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(199903)6:2<115::aid-nla151>3.0.co;2-8
Subject(s) - mathematics , finite element method , lagrange multiplier , computation , mathematical analysis , isothermal process , multiplier (economics) , constraint algorithm , numerical analysis , mathematical optimization , thermodynamics , algorithm , physics , macroeconomics , economics
For a generalized Stokes problem it is shown that weak solvability is equivalent to ellipticity of the system. In the case of ellipticity, the standard mixed finite element method converges if a Babuska‐Brezzi condition for the pressure‐form holds. This result is also true if the pressure operator is not the Lagrangean multiplier of the constraint. The results are applied to a non‐isothermal gas flow in metalorganic chemical vapor deposition (MOCVD) reactors. Some numerical computations using Uzawa's method are given. Copyright © 1999 John Wiley & Sons, Ltd.