On discrétise en temps, par le schéma Chorin–Temam, un problème de Stokes non stationnaire posé dans (), étant donnés : trouver solution de , et (1). En sʼinspirant des analyses de C. Bernardi et de R. Verfürth pour le schéma Euler rétrograde, nous construisons des estimateurs a posteriori pour lʼerreur commise sur en norme . Notre étude est étayée par des expériences numériques.
We consider the Chorin–Temam scheme (the simplest pressure-correction projection method) for the time discretization of an unstationary Stokes problem in () given : find solution to , and:
(1) |
Accepté le :
Publié le :
Sébastien Boyaval 1, 2 ; Marco Picasso 3
@article{CRMATH_2013__351_23-24_931_0, author = {S\'ebastien Boyaval and Marco Picasso}, title = {A posteriori analysis of the {Chorin{\textendash}Temam} scheme for {Stokes} equations}, journal = {Comptes Rendus. Math\'ematique}, pages = {931--936}, publisher = {Elsevier}, volume = {351}, number = {23-24}, year = {2013}, doi = {10.1016/j.crma.2013.10.026}, language = {en}, }
TY - JOUR AU - Sébastien Boyaval AU - Marco Picasso TI - A posteriori analysis of the Chorin–Temam scheme for Stokes equations JO - Comptes Rendus. Mathématique PY - 2013 SP - 931 EP - 936 VL - 351 IS - 23-24 PB - Elsevier DO - 10.1016/j.crma.2013.10.026 LA - en ID - CRMATH_2013__351_23-24_931_0 ER -
Sébastien Boyaval; Marco Picasso. A posteriori analysis of the Chorin–Temam scheme for Stokes equations. Comptes Rendus. Mathématique, Volume 351 (2013) no. 23-24, pp. 931-936. doi : 10.1016/j.crma.2013.10.026. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.10.026/
[1] A posteriori error analysis of the fully discretized time-dependent Stokes equations, M2AN Math. Model. Numer. Anal., Volume 38 (2004), pp. 437-455
[2] Numerical solution of the Navier–Stokes equations, Math. Comput., Volume 22 (1968), pp. 754-762
[3] Finite Element Approximation of the Navier–Stokes Equations, Lecture Notes in Mathematics, vol. 749, Springer-Verlag, Berlin, 1979
[4] Some implementations of projection methods for Navier–Stokes equations, RAIRO Modél. Math. Anal. Numér., Volume 30 (1996), pp. 637-667
[5] An overview of projection methods for incompressible flows, Comput. Methods Appl. Mech. Eng., Volume 195 (2006), pp. 6011-6045
[6] On stability and convergence of projection methods based on pressure Poisson equation, Int. J. Numer. Methods Fluids, Volume 26 (1998), pp. 1039-1053
[7] Time error estimators for the Chorin–Temam scheme, ARIMA, Volume 13 (2010), pp. 33-46
[8] A posteriori error analysis of time-dependent Stokes problem by Chorin–Temam scheme, Calcolo (2011), pp. 1-21 | DOI
[9] Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier–Stokes Equations, Advances in Numerical Mathematics, B.G. Teubner GmbH, Stuttgart, 1997
[10] Une méthode dʼapproximation de la solution des équations de Navier–Stokes, Bull. Soc. Math. Fr., Volume 96 (1968), pp. 115-152
[11] Navier–Stokes Equations, Studies in Mathematics and Its Applications, vol. 2, North-Holland Publishing Co., Amsterdam, 1979
[12] A posteriori error analysis of space–time finite element discretizations of the time-dependent Stokes equations, Calcolo, Volume 47 (2010), pp. 149-167
Cité par Sources :
Commentaires - Politique