Subgrid Stabilization of Galerkin Approximations of Linear Contraction Semi-Groups of Class C0 in Hilbert Spaces

Numerical Methods for Partial Differential Equations

Volumn 17, Issue 1, 2001, Pages 1-25

  Guermond, Jean Luc ^a  

^a CNRS   (France)

Author keywords

Artificial viscosity; Finite elements; Galerkin methods; Linear hyperbolic equations; Multiscale methods; Semi groups; Stabilization; Subgrid modeling

Indexed keywords

EID: 0042830506     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/1098-2426(200101)17:1<1::AID-NUM1>3.0.CO;2-1     Document Type: Article

References (23)

1. P. Brenner, M. Crouzeix, and V. Thomée, Single step methods for inhomogeneous linear differential equations in Banach spaces, RAIRO Anal Numer 16 (1982), 5-26.
2. P. Lesaint and P. A. Raviart, "On a finite element method for solving the neutron transport equation," Mathematical aspects of finite elements in partial differential equations, C. de Boors (Editor), Academic, New York, 1974, pp. 89-123.
3. C. Johnson and J. Pitkäranta, An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation, Math Comp 46 (1986), 1-26.
4. C. Johnson, U. Nävert, and J. Pitkäranta, Finite element methods for linear hyperbolic equations, Comp Meth Appl Mech Eng 45 (1984), 285-312.
5. J. L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Dunod, Paris, 1968,
6. 2 AN), 33 (1999), 1293-1316.
7. J.-L. Guermond, Subgrid stabilizations of Galerkin approximations of monotone operators, Zeitschrift für angewandte Mathematik und Mechanik, ZAMM 79 (1999), 29-32.
8. J. Smagorinsky, General circulation experiments with the primitive equations. I. The basic experiments, J Atmos Sci 32 (1963), 680-689.
9. E. Tadmor, Convergence of spectral methods for nonlinear conservation laws, SIAM J Numer Anal 26 (1989), 30-44.
10. C. Foias, O. P. Manley, and R. Temam, Modelization of the interaction of small and large eddies in two-dimensional turbulent flows, Math Mod Num Anal 22 (1988), 93-114.
11. M. Marion and R. Temam, Nonlinear Galerkin methods: the finite element case, Numer Math 57 (1990), 1-22.
12. D. N. Arnold, F. Brezzi, and M. Fortin, A stable finite element for the Stokes equations, Calcolo 21 (1984), 337-344.
13. F. Brezzi, M. O. Bristeau, L. Franca, M. Mallet, and G. Rogé, A relationship between stabilized finite element methods and the Galerkin method with bubble functions, Comp Meth Appl Mech Eng 96 (1992), 117-129.
14. C. Baiocchi, F. Brezzi, and L. P. Franca, Virtual bubbles and Galerkin-least-square type methods (Ga.L.S), Comp Meth Appl Mech Eng 105 (1993), 125-141.
15. M. Crouzeix and P. A. Raviart, Conforming and nonconforming finite element methods for solving the stationnary Stokes equations, RAIRO 3 (1973), 33-75.
16. H. Brezis, Analyse fonctionnelle, théorie et applications, Masson, Paris, 1983.
17. K. Yosida, Functional analysis, SCSM 123, Sixth edition, Springer-Verlag, New York, 1980.
18. V. Girault and P. A. Raviart, Finite element methods for Navier-Stokes equations, Springer Series in Comp Math 5, Springer-Verlag, New York, 1986.
19. Y. Maday, S. M. Ould Kaber, and E. Tadmor, Legendre pseudo-spectral viscosity method for nonlinear conservation laws, SIAM J Numer Anal 30 (1993), 321-342.
20. G. Zhou, How accurate is the streamline diffusion finite element method? Math Comp 66 (1997), 31-44.
21. C. W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, II. J Comp Phys 83 (1989), 32-78.
22. J. Goodman, A. Kurganov, and P. Rosenau, Breakdown in Burgers-type equations with saturating dissipation fluxes, Nonlinearity 12 (1999), 247-268.
23. J.-L. Guermond and L. Quartapelle, A projection FEM for variable density incompressible flows, J Comp Phys, to appear.