@article{M2AN_1999__33_6_1293_0, author = {Guermond, Jean-Luc}, title = {Stabilization of Galerkin approximations of transport equations by subgrid modeling}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {33}, year = {1999}, pages = {1293-1316}, mrnumber = {1736900}, zbl = {0946.65112}, language = {en}, url = {http://dml.mathdoc.fr/item/M2AN_1999__33_6_1293_0} }
Guermond, Jean-Luc. Stabilization of Galerkin approximations of transport equations by subgrid modeling. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 33 (1999) pp. 1293-1316. http://gdmltest.u-ga.fr/item/M2AN_1999__33_6_1293_0/
[1] Nonlinear Galerkin methods and mixed finite elements : two-grid algorithms for the Navier-Stokes equations Numer. Math. 68 (1994) 189-213. | MR 1283337 | Zbl 0811.76035
and ,[2] A stable finite element for the Stokes equations Calcolo 21 (1984) 337-344. | MR 799997 | Zbl 0593.76039
, and ,[3] 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 1387427 | Zbl 0852.76073
and ,[4] Virtual bubbles and Galerkin-least-square type methods (Ga. L. S.) Comput. Methods Appl. Mech. Engrg 105 (1993) 125-141. | MR 1222297 | Zbl 0772.76033
, and ,[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 274925 | Zbl 0202.36903
,[6] Mémoire de DEA. Analyse Numérique, Paris XI, Internal report LIMSI (1999).
,[7] Relationship between stabihzed finite element methods and the Galerkin method with bubble functions. Comput. Methods Appl. Mech. Engrg. 96 (1992) 117-129. | MR 1159592 | Zbl 0756.76044
, , , and ,[8] 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 679322 | Zbl 0497.76041
and ,[9] Conforming and nonconforming finite element methods for solving the stationary Stokes equations RAIRO Anal. Numér 7 (1973) 33-76. | Numdam | MR 343661 | Zbl 0302.65087
and ,[10] Comparison of some finite element methods for solving the diffusion-convection-reaction equations. Comput. Methods Appl. Mech. Engrg. 156 (1997) 185-210. | MR 1622508 | Zbl 0959.76040
,[11] 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 672564 | Zbl 0492.65051
and ,[12] Analyse mathématique et calcul numérique pour les sciences et les techniques Masson, Paris (1984). | Zbl 0642.35001
and ,[13] Modelization of the interaction of small and large eddies in two dimensional turbulent flows, Math. Modelling Numer. Anal. 22 (1988) 93-114. | Numdam | Zbl 0663.76054
, and[14] An analysis of the convergence of mixed Finite Element Methods RAIRO Anal. Numér. 11 (1977) 341-354. | Numdam | MR 464543 | Zbl 0373.65055
,[15] Bubble functions prompt unusual stabilized finite element methods Comput. Methods Appl. Mech. Engrg. 123 (1994) 299-308. | MR 1339376 | Zbl 1067.76567
and ,[16] A dynamic subgrid-scale eddy viscosity model Phys. Fluids A 3 (1991) 1760-1765. | Zbl 0825.76334
, , and ,[17] Finite Element Methods for Navier-Stokes Equations Springer Ser. Comput Math. 5, Springer-Verlag (1986). | MR 851383 | Zbl 0585.65077
and ,[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 1680045 | Zbl 0933.65058
,[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 1365381 | Zbl 0866.76044
,[20] Finite element methods for linear hyperbolic equations Comput. Methods Appl. Mech. Engrg. 45 (1984) 285-312. | MR 759811 | Zbl 0526.76087
, , ,[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] Nonlinear Galerkin methods : the finite element case Numer. Math. 57 (1990) 1-22. | MR 1057121 | Zbl 0702.65081
and ,[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 1083327 | Zbl 0729.65085
,[24] On the transport-diffusion algorithm and its applications to the Navier Stokes equations. Numer. Math. 38 (1982) 309-332. | MR 654100 | Zbl 0505.76100
,[25] Numerical Approximation of Partial Differential Equations. Springer Ser. Comput. Math. 23, Springer-Verlag (1994). | MR 1299729 | Zbl 0803.65088
and ,[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 951325 | Zbl 0637.76024
,[28] Postprocessing the Galerkin method : a novel approach to Approximate Inertial Manifolds. SIAM J. Numer. Anal. 35 (1998) 941-972. | MR 1619914 | Zbl 0914.65105
, and ,[29] How accurate is the streamline diffusion finite element method ? Math. Comp. 66 (1997) 31-44. | MR 1370859 | Zbl 0854.65094
,