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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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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