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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Optimal error estimate of the penalty finite element method for the time-dependent Navier-Stokes equations
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by Yinnian He PDF
Math. Comp. 74 (2005), 1201-1216 Request permission


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:
  • 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
  • © Copyright 2005 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 1201-1216
  • MSC (2000): Primary 35L70, 65N30, 76D06
  • DOI:
  • MathSciNet review: 2136999