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Analysis of a sequential regularization method for the unsteady Navier-Stokes equations
Author(s):
Xiliang
Lu;
Ping
Lin;
Jian-Guo
Liu.
Journal:
Math. Comp.
77
(2008),
1467-1494.
MSC (2000):
Primary 65M12;
Secondary 76D05
Posted:
February 1, 2008
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Abstract:
The incompressibility constraint makes Navier-Stokes equations difficult. A reformulation to a better posed problem is needed before solving it numerically. The sequential regularization method (SRM) is a reformulation which combines the penalty method with a stabilization method in the context of constrained dynamical systems and has the benefit of both methods. In the paper, we study the existence and uniqueness for the solution of the SRM and provide a simple proof of the convergence of the solution of the SRM to the solution of the Navier-Stokes equations. We also give error estimates for the time discretized SRM formulation.
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Additional Information:
Xiliang
Lu
Affiliation:
Department of Mathematics, National University of Singapore, Science Drive 2, Singapore 117543, Singapore
Address at time of publication:
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenberger Strasse 69, A-4040 Linz, Austria
Email:
lu_xiliang@hotmail.com
Ping
Lin
Affiliation:
Department of Mathematics, National University of Singapore, Science Drive 2, Singapore 117543, Singapore
Email:
matlinp@nus.edu.sg
Jian-Guo
Liu
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742-4015
Email:
jliu@math.umd.edu
DOI:
10.1090/S0025-5718-08-02087-5
PII:
S 0025-5718(08)02087-5
Keywords:
Navier-Stokes equations,
iterative penalty method,
implicit parabolic PDE,
error estimates,
constrained dynamical system,
stabilization method
Received by editor(s):
July 25, 2006
Received by editor(s) in revised form:
June 4, 2007
Posted:
February 1, 2008
Additional Notes:
The research was supported by several grants at the Department of Mathematics, National University of Singapore
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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