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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Optimal error estimate of the penalty finite element method for the time-dependent Navier-Stokes equations


Author: Yinnian He
Journal: Math. Comp. 74 (2005), 1201-1216
MSC (2000): Primary 35L70, 65N30, 76D06
Published electronically: February 16, 2005
MathSciNet review: 2136999
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Abstract: A fully discrete penalty finite element method is presented for the two-dimensional time-dependent Navier-Stokes equations. The time discretization of the penalty Navier-Stokes equations is based on the backward Euler scheme; the spatial discretization of the time discretized penalty Navier-Stokes equations is based on a finite element space pair $(X_h,M_h)$which satisfies some approximate assumption. An optimal error estimate of the numerical velocity and pressure is provided for the fully discrete penalty finite element method when the parameters $\epsilon,~\Delta t$ and $h$ are sufficiently small.


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Additional Information

Yinnian He
Affiliation: Faculty of Science, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China
Email: heyn@mail.xjtu.edu.cn

DOI: http://dx.doi.org/10.1090/S0025-5718-05-01751-5
PII: S 0025-5718(05)01751-5
Keywords: Navier-Stokes problem, penalty finite element method, backward Euler scheme, error estimate
Received by editor(s): July 2, 2003
Received by editor(s) in revised form: May 15, 2004
Published electronically: February 16, 2005
Additional Notes: This work was subsidized by the Special Funds for Major State Basic Research Projects G1999032801-07, NSF of China 10371095
Article copyright: © Copyright 2005 American Mathematical Society