An adaptive multi-level method for convection diffusion problems

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1. [1] M. Bercovier, O. Pironneau and V. Sastri, Finite elements and characteristics for some parabolic-hyperbolic problems. Appl. Math. Modelling 7 (1983) 89-96. Zbl0505.65055MR703386
2. [2] K. Boukir, Y. Maday, B. Metivet and R. Razafindrakoto, A high-order characteristics/finite element method for imcompressible Navier-Stokes equations. Rapport de l'Université Pierre et Marie Curie, R92032 (1992). Zbl0904.76040
3. [3] J. B. Burie and M. Marion, Multi-level methods in space and time for Navier-Stokes equations. SIAM J. Numer. Anal. 34 (1997) 1574-1599. Zbl0897.76070MR1461797
4. [4] J. B. Burie and M. Marion, Adaptative multi-level methods in space and time for paraboloc problems- The periodic case. Math. of Comp. (to appear). Zbl0941.65101MR1648359
5. [5] A. Debussche, T. Dubois and R. Temam, The nonlinear Galerkin method: A multi-scale method applied to the simulation of turbulent flows. Theoret. Comput. Fluid Dynamics 7 (1995) 279-315. Zbl0838.76060
6. [6] J. Douglas and T.F. Russel, Numerical methods for convection dominated diffusion problems based on combining the method of caracteristics with finite element methods or finite difference method. SIAM J. Numer. Anal. 19 (1982) 871-885. Zbl0492.65051MR672564
7. [7] T. Dubois, Simulation numérique d'écoulement homogènes et non-homogènes par des méthodes multi-résolution, Thèse, Université Paris-Sud (1993). 
8. [8] K. Enksson and C. Johnson, Adaptative finite element methods for parabolic problems I : A linear model problem. SIAM J. Numer. Anal. 28 (1991) 43-77. Zbl0732.65093MR1083324
9. [9] C. Foras, O. Manley and R. Temam, Modelling of the interaction of small and large eddies in two-dimensional turbulent flows. M2AN 22 (1998) 93-114. Zbl0663.76054MR934703
10. [10] P. Houston and E. Suli, Adaptative Lagrange-Galerkin methods for unsteady convection-dominated diffusion problems, Oxford University Computing Laboratory Report, 95/24 (1995). Zbl0957.65085
11. [11] F. Jauberteau, Résolution numérique des équations de Navier-Stokes instationnaires par méthodes spectrales. Méthode de Galerkin non linéaire, Thèse, Université Paris-Sud (1990). 
12. [12] M. Marion and A. Mollard, A multi-level characteristics method for periodic convection-dominated diffusion problems. Numer. Math. PDEs (to appear). Zbl0953.65065
13. [13] M. Marion and J. Xu, Error estimates on a new nonlinear Galerkin method based on two-grid finite elements. SIAM J. Numer. Anal. 32 (1995) 1170-1184. Zbl0853.65092MR1342288
14. [14] A. Mollard, Méthodes de caractéristiques multi-niveaux en espace et en temps pour une équation de convection-diffusion - Cas d'une approximation pseudo-spectrale, Thèse, École Centrale de Lyon (1998). 
15. [15] O. Pironneau, Finite element methods for fluids, Masson (1989). Zbl0748.76003MR1030279
16. [16] E. Suli, Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes Equations. Numer. Math. 53 (1988) 459-483. Zbl0637.76024MR951325
17. [17] E. Suli and A. F. Ware, A spectral method of characteristics for hyperbolic problems. SIAM J. Numer. Anal. 28 (1991) 423-445. Zbl0743.65080MR1087513