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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2011; 48(3): 529-550

Printed May 1, 2011

https://doi.org/10.4134/JKMS.2011.48.3.529

Copyright © The Korean Mathematical Society.

An a posteriori error estimate for mixed finite element approximations of the Navier-Stokes equations

Abdeslam Elakkad, Ahmed Elkhalfi, and Najib Guessous

Facult\'e des Sciences et Techniques B. P. 2202, Facult\'e des Sciences et Techniques B. P. 2202, Ecole normale Sup\'erieure de F\`es

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In this work, a numerical solution of the incompressible Navier-Stokes equations is proposed. The method suggested is based on an algorithm of discretization by mixed finite elements with a posteriori error estimation of the computed solutions. In order to evaluate the performance of the method, the numerical results are compared with some previously published works or with others coming from commercial code like Adina system.

Keywords: incompressible Navier-Stokes equations, mixed finite element method, a posteriori error estimates, iterative solvers, Adina system

MSC numbers: 49K05, 49K15, 49S05

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