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The effect of the stability of mixed finite element approximations on the accuracy and rate of convergence of solution when solving incompressible flow problems
Author(s) -
Silvester D. J.,
Thatcher R. W.
Publication year - 1986
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650061106
Subject(s) - stability (learning theory) , convergence (economics) , mathematics , compressibility , incompressible flow , rate of convergence , finite element method , flow (mathematics) , mathematical analysis , mechanics , geometry , physics , thermodynamics , computer science , channel (broadcasting) , machine learning , economics , economic growth , computer network
The stability of two different mixed finite element methods for incompressible flow problems are theoretically analysed. The effect of the stability of the mixed approximation on the accuracy and the rate of convergence of solution is assessed for two non‐trivial problems. The numerical results presented indicate that if the stability of the mixed approximation is not guaranteed then both pressure and velocity solutions are markedly less accurate. In one of the cases considered the ultimate convergence of both the pressure and the velocity solutions is seriously in doubt.