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Penalty finite element approximations for the Stokes equations by L 2 projection
Author(s) -
Li Jian
Publication year - 2008
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1051
Subject(s) - finite element method , mathematics , penalty method , projection (relational algebra) , space (punctuation) , mathematical analysis , order (exchange) , element (criminal law) , mathematical optimization , algorithm , physics , computer science , law , finance , political science , economics , thermodynamics , operating system
This paper considers the penalty finite element method for the Stokes equations, based on some stable finite elements space pair ( X h , M h ) that do satisfy the discrete inf–sup condition. Theoretical results show that the penalty error converges as fast as one should expect from the order of the elements. Moreover, the penalty finite element method by L 2 projection can improve the penalty error estimates. Finally, we confirm these results by a series of numerical experiments. Copyright © 2008 John Wiley & Sons, Ltd.