Mathematics of Computation

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

Author(s): Yinnian He.
Journal: Math. Comp. 74 (2005), 1201-1216.
MSC (2000): Primary 35L70, 65N30, 76D06
Posted: February 16, 2005
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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

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

are sufficiently small.

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Retrieve articles in Mathematics of Computation with MSC (2000): 35L70, 65N30, 76D06

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: 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
Posted: 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
Copyright of article: Copyright 2005, American Mathematical Society

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