A posteriori analysis of iterative algorithms for Navier–Stokes problem
Bernardi, Christine1 ; Dakroub, Jad1, 2 ; Mansour, Gihane2 ; Sayah, Toni2
1 Laboratoire Jacques-Louis Lions - C.N.R.S. et Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris cedex 05, France.
2 Unité de recherche EGFEM, Faculté des sciences, Université Saint-Joseph, Lebanon, Beirut, Liban.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 4, pp. 1035-1055.

This work deals with a posteriori error estimates for the Navier–Stokes equations. We propose a finite element discretization relying on the Galerkin method and we solve the discrete problem using an iterative method. Two sources of error appear, the discretization error and the linearization error. Balancing these two errors is very important to avoid performing an excessive number of iterations. Several numerical tests are provided to evaluate the efficiency of our indicators.

Reçu le :
DOI : 10.1051/m2an/2015062
Classification : 65N30, 65N15, 65J15, 76D05
Mots-clés : A posteriori error estimation, Navier–Stokes problem, iterative method
Bernardi, Christine 1 ; Dakroub, Jad 1, 2 ; Mansour, Gihane 2 ; Sayah, Toni 2

1 Laboratoire Jacques-Louis Lions - C.N.R.S. et Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris cedex 05, France.
2 Unité de recherche EGFEM, Faculté des sciences, Université Saint-Joseph, Lebanon, Beirut, Liban. 
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     title = {A posteriori analysis of iterative algorithms for {Navier{\textendash}Stokes} problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1035--1055},
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Bernardi, Christine; Dakroub, Jad; Mansour, Gihane; Sayah, Toni. A posteriori analysis of iterative algorithms for Navier–Stokes problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 4, pp. 1035-1055. doi : 10.1051/m2an/2015062. http://www.numdam.org/articles/10.1051/m2an/2015062/

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