@article{M2AN_1999__33_6_1293_0,
author = {Guermond, Jean-Luc},
title = {Stabilization of {Galerkin} approximations of transport equations by subgrid modeling},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {1293--1316},
publisher = {EDP-Sciences},
volume = {33},
number = {6},
year = {1999},
mrnumber = {1736900},
zbl = {0946.65112},
language = {en},
url = {http://www.numdam.org/item/M2AN_1999__33_6_1293_0/}
}
TY - JOUR AU - Guermond, Jean-Luc TI - Stabilization of Galerkin approximations of transport equations by subgrid modeling JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1999 SP - 1293 EP - 1316 VL - 33 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/item/M2AN_1999__33_6_1293_0/ LA - en ID - M2AN_1999__33_6_1293_0 ER -
%0 Journal Article %A Guermond, Jean-Luc %T Stabilization of Galerkin approximations of transport equations by subgrid modeling %J ESAIM: Modélisation mathématique et analyse numérique %D 1999 %P 1293-1316 %V 33 %N 6 %I EDP-Sciences %U http://www.numdam.org/item/M2AN_1999__33_6_1293_0/ %G en %F M2AN_1999__33_6_1293_0
Guermond, Jean-Luc. Stabilization of Galerkin approximations of transport equations by subgrid modeling. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 6, pp. 1293-1316. http://www.numdam.org/item/M2AN_1999__33_6_1293_0/
[1] and , Nonlinear Galerkin methods and mixed finite elements : two-grid algorithms for the Navier-Stokes equations Numer. Math. 68 (1994) 189-213. | MR | Zbl
[2] , and , A stable finite element for the Stokes equations Calcolo 21 (1984) 337-344. | MR | Zbl
[3] and , Inégalité de Poincaré courbe pour le traitement variationnel de l'équation de transport C. R.Acad.Sci. Paris Sér. I 322 (1996) 721-727. | MR | Zbl
[4] , and , Virtual bubbles and Galerkin-least-square type methods (Ga. L. S.) Comput. Methods Appl. Mech. Engrg 105 (1993) 125-141. | MR | Zbl
[5] , Problèmes aux limites pour les équations aux dérivées partielles du premier ordre à coefficients réels, théorèmes d'approximation, application à l'équation de transport Ann. Sci. École Norm. Sup. Sér. IV 3 (1970) 185-233. | Numdam | MR | Zbl
[6] , Mémoire de DEA. Analyse Numérique, Paris XI, Internal report LIMSI (1999).
[7] , , , and , Relationship between stabihzed finite element methods and the Galerkin method with bubble functions. Comput. Methods Appl. Mech. Engrg. 96 (1992) 117-129. | MR | Zbl
[8] and , Streamline Upwind/Petrov-Galerkin formulations for convective dominated flows with particular emphasis on the incompressible Navier-Stokes equations Comput. Methods. Appl. Mech. Engrg 32 (1982) 199-259. | MR | Zbl
[9] and , Conforming and nonconforming finite element methods for solving the stationary Stokes equations RAIRO Anal. Numér 7 (1973) 33-76. | Numdam | MR | Zbl
[10] , Comparison of some finite element methods for solving the diffusion-convection-reaction equations. Comput. Methods Appl. Mech. Engrg. 156 (1997) 185-210. | MR | Zbl
[11] and , Numerical methods for convection dominated diffusion problems based on combinig the method of characteristics with finite element methods or finite difference method SIAM J. Numer. Anal. 19 (1982) 871-885. | MR | Zbl
[12] and , Analyse mathématique et calcul numérique pour les sciences et les techniques Masson, Paris (1984). | Zbl
[13] , and Modelization of the interaction of small and large eddies in two dimensional turbulent flows, Math. Modelling Numer. Anal. 22 (1988) 93-114. | Numdam | Zbl
[14] , An analysis of the convergence of mixed Finite Element Methods RAIRO Anal. Numér. 11 (1977) 341-354. | Numdam | MR | Zbl
[15] and , Bubble functions prompt unusual stabilized finite element methods Comput. Methods Appl. Mech. Engrg. 123 (1994) 299-308. | MR | Zbl
[16] , , and , A dynamic subgrid-scale eddy viscosity model Phys. Fluids A 3 (1991) 1760-1765. | Zbl
[17] and , Finite Element Methods for Navier-Stokes Equations Springer Ser. Comput Math. 5, Springer-Verlag (1986). | MR | Zbl
[18] , Stabilisation par viscosité de sous-maille pour l'approximation de Galerkin des opérateurs monotones C. R. Acad. Sci. Paris Sér. I 328 (1999) 617-622. | MR | Zbl
[19] , Multiscale phenomena Green's function, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized formulations Comput. Methods Appl. Mech. Engrg. 127 (1995) 387-401. | MR | Zbl
[20] , , , Finite element methods for linear hyperbolic equations Comput. Methods Appl. Mech. Engrg. 45 (1984) 285-312. | MR | Zbl
[21] , Modification of the Navier-Stokes equations for large velocity gradients Boundary Value Problems of Mathematical Physics and Related Aspects of Function Theory, Consultants bureau, New-York (1970).
[22] and , Nonlinear Galerkin methods : the finite element case Numer. Math. 57 (1990) 1-22. | MR | Zbl
[23] , A note on the convergence of the discontinuous Galerkin method for a scalar hyperbolic equation. SIAM J. Numer. Anal 28 (1991) 133-140. | MR | Zbl
[24] , On the transport-diffusion algorithm and its applications to the Navier Stokes equations. Numer. Math. 38 (1982) 309-332. | MR | Zbl
[25] and , Numerical Approximation of Partial Differential Equations. Springer Ser. Comput. Math. 23, Springer-Verlag (1994). | MR | Zbl
[26] , General circulation experiments with the primitive equations. I. The basic experiments. J. Atmospheric Sei. 2 (1963) 680-689.
[27] , Convergence and non-linear stability of the Lagrange-Galerkin method for the Navier-Stokes equations Numer, Math. 3 (1988) 459-483. | MR | Zbl
[28] , and , Postprocessing the Galerkin method : a novel approach to Approximate Inertial Manifolds. SIAM J. Numer. Anal. 35 (1998) 941-972. | MR | Zbl
[29] , How accurate is the streamline diffusion finite element method ? Math. Comp. 66 (1997) 31-44. | MR | Zbl
