Stabilized finite element method for the Rayleigh-Benard equations with infinite Prandtl number in a spherical shell

Computer Methods in Applied Mechanics and Engineering

Volumn 190, Issue 3-4, 2000, Pages 387-402

  Tabata, M ^a   Suzuki, A ^a  

^a KYUSHU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

BUOYANCY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; DIFFUSION IN SOLIDS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PRANDTL NUMBER; SHELLS (STRUCTURES);

RAYLEIGH-BENARD EQUATIONS; STOKES EQUATION;

HEAT CONVECTION;

CONVECTION; FINITE ELEMENT METHOD; GEOPHYSICAL FLUID DYNAMICS;

FINITE ELEMENT METHOD; GEOPHYSICS; MANTLE CONVECTION;

EID: 0034287407     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(00)00209-7     Document Type: Article

References (25)

1. I. Babuška, The theory of small changes in the domain of existence in the theory of partial differential equations and its applications, in: I. Babuška (Ed.), Differential Equations and Their Applications, Czechoslovak Academy of Sciences, 1963, pp. 13-26.
2. J.R. Baumgardner, Three-dimensional treatment of convective flow in the Earth's mantle, J. Stat. Phys. 39 (1985) 501-511.
3. D. Bercovici, G. Schubert, G.A. Glatzmaier, A. Zebib, Three-dimensional thermal convection in a spherical shell, J. Fluid Mech. 206 (1989) 75-104.
4. J. Boland, W. Layton, An analysis of the finite element method for natural convection problems, Numer. Methods Partial Differential Equations 6 (1990) 115-126.
5. J. Boland, W. Layton, Error analysis for finite element methods for steady natural convection problems, Numer. Funct. Anal. Optim. 11 (1990) 449-483.
6. A.N. Brooks, T.J.R. Hughes, Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg. 32 (1982) 199-259.
7. P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
8. P. Clément, Approximation of finite element functions using local regularizaton, Rev. Françaisc Automat. Informat. Recherche Opérationelle Sér. Rouge Anal. Numér. 9 (1975) 77-84.
9. J. Douglas, J. Wang, An absolutely stabilized finite element method for the Stokes problem, Math. Comp. 52 (1989) 495-508.
10. L.P. Franca, S.L. Frey, T.J.R. Hughes, Stabilized finite element methods: I. Application to the advective-diffusive model, Comput. Methods Appl. Mech. Engrg. 95 (1992) 253-276.
11. L.P. Franca, R. Stenberg, Error analysis of some Galerkin least squares methods for the elasticity equations, SIAM J. Numer. Anal. 28 (1991) 1680-1697.
12. V. Girault, P.A. Raviart, Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms, Springer, Berlin, 1986.
13. T.J.R. Hughes, L.P. Franca, A new finite element formulation for computational fluid dynamics:VII. The Stokes problem with various well-posed boundary conditions:Symmetric formulations that converge for all velocity/pressure spaces, Comput. Methods Appl. Mech. Engrg. 65 (1987) 85-96.
14. T.J.R. Hughes, L.P. Franca, G.M. Hulbert, A new finite element formulation for computational fluid dynamics:VIII The Galerkin/least-squares method for advective-diffusive equations, Comput. Methods Appl. Mech. Engrg. 73 (1989) 173-189.
15. H. Itoh, Numerical simulation of thermal convection in a fluid with the infinite Prandtl number and its application to a glass manufacturing problem, Hiroshima Math. J. 29 (1999) 27-60.
16. H. Itoh, M. Tabata, A finite element analysis for a thermal convection problem with the infinite Prandtl number, Hiroshima Math. J. 28 (1998) 555-570.
17. J.L. Lions, Quelques méthodes de résolution des problèmes aux limites nonlinéaires, Dunod, Paris, 1969.
18. Y. Iwase, Three-dimensional infinite Prandtl number convection in a spherical shell with temperature-dependent viscosity, J. Geomag. Geoelectr. 48 (1996) 1499-1514.
19. J.T. Ratcliff, G. Schubert, A. Zebib, Steady tetrahedral and cubic patterns of spherical shell convection with temperature-dependent viscosity, J. Geophys. Res. 101 (1996) 25473-25484.
20. M. Tabata, Finite element approximation to infinite Prandtl number Boussinesq equations with slip boundary condition, in: K.D. Papailiou et al. (Eds.), Computational Fluid Dynamics'98, Wiley, New York, 1998, pp. 22-27.
21. M. Tabata, Slip boundary conditions and rigid body movements in finite element analysis, Kyushu Univ. Preprint Ser. Math. 99-2 (1999).
22. M. Tabata, D. Tagami, Error estimates of drag and lift in nonstationary Navier-Stokes flows. Kyushu Univ. Preprint Ser. Math. 99-11 (1999).
23. R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam, 1984.
24. R. Verfürth, Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition, Numer. Math. 50 (1987) 697-721.
25. A. Zebib, Linear and weakly nonlinear variable viscosity convection in spherical shells, Theoret. Comput. Fluid Dynamics 4 (1993) 241-253.