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Local projection stabilization of equal order interpolation applied to the Stokes problem
Author(s):
Sashikumaar
Ganesan;
Gunar
Matthies;
Lutz
Tobiska.
Journal:
Math. Comp.
77
(2008),
2039-2060.
MSC (2000):
Primary 65N12;
Secondary 65N30
Posted:
May 9, 2008
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Additional information
Abstract:
The local projection stabilization allows us to circumvent the Babuška-Brezzi condition and to use equal order interpolation for discretizing the Stokes problem. The projection is usually done in a two-level approach by projecting the pressure gradient onto a discontinuous finite element space living on a patch of elements. We propose a new local projection stabilization method based on (possibly) enriched finite element spaces and discontinuous projection spaces defined on the same mesh. Optimal order of convergence is shown for pairs of approximation and projection spaces satisfying a certain inf-sup condition. Examples are enriched simplicial finite elements and standard quadrilateral/hexahedral elements. The new approach overcomes the problem of an increasing discretization stencil and, thus, is simple to implement in existing computer codes. Numerical tests confirm the theoretical convergence results which are robust with respect to the user-chosen stabilization parameter.
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Additional Information:
Sashikumaar
Ganesan
Affiliation:
Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany
Email:
ga.sashikumaar@mathematik.uni-magdeburg.de
Gunar
Matthies
Affiliation:
Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstrasse 150, D-44780 Bochum, Germany
Email:
gunar.matthies@ruhr-uni-bochum.de
Lutz
Tobiska
Affiliation:
Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany
Email:
tobiska@mathematik.uni-magdeburg.de
DOI:
10.1090/S0025-5718-08-02130-3
PII:
S 0025-5718(08)02130-3
Received by editor(s):
April 17, 2007
Received by editor(s) in revised form:
September 21, 2007
Posted:
May 9, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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