Scales of ε-uniform a priori estimates for nonstationary convection-dominated diffusion problems

Annali dell'Universita di Ferrara

Volumn 46, Issue 1, 2000, Pages 115-137

  Bause, Markus ^a  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347048447     PISSN: 04303202     EISSN: 18271510     Source Type: Journal    
DOI: 10.1007/BF02837293     Document Type: Article

References (25)

1. M. Bause, Optimum convergence rates for fully discretized Navier-Stokes approximations of higher order in Lipschitz domains (in German), Ph. D. thesis, University of Paderborn, Paderborn, 1997.
2. M. Bause-P. Knabner, Uniform error analysis for Lagrange-Galerkin approximations of convection-dominated diffusion problems. Part I: A priori analysis in Lagrangian coordinates and optimal order error estimates for the time discretization, submitted to: SIAM J. Numer. Anal., 1999.
3. M. Bause-P. Knabner, Uniform convergence rates for Eulerian and Lagrangian finite element approximations of convection-dominated diffusion problems, in: The Proceedings of the International Conference on Numerical Methods for Transport-Dominated and Related Problems, EPSICODE '99 (Magdeburg 1999), Computing, submitted.
4. M. Bause-P. Knabner, Uniform error analysis for Lagrange-Galerkin approximations of convection-dominated diffusion problems. Part II: Time discretization for rough initial values, error estimates for the spatial discretization and numerical results, submitted to SIAM J. Numer. Anal., 2000.
5. A. J. Chorin-J. E. Marsden, A mathematical introduction to fluid mechanics, Springer, New York, 1984.
6. J. Douglas-T. F. Russell, Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures, SIAM J. Numer. Anal. 19 (1982), pp. 871-885.
7. J. Douglas-C. S. Huang-F. Pereira, The modified method of characteristics with adjusted advection, Numer. Math., 83 (1999), pp. 353-368.
8. R. E. Ewing, The mathematics of reservoir simulation, SIAM, Philadelphia, 1983.
9. A. Friedman, Partial differential equations, Krieger, New York, 1976.
10. H. Fujita-T. Suzuki, Evolution problems, in P. G. Ciarlet and J. L. Lions (eds.): Handbook of numerical analysis, Vol. II, Finite element methods (Part 1), North-Holland, Amsterdam, 1991.
11. P. Grisvard, Elliptic problems in nonsmooth domains, Pitman, Boston, 1985.
12. P. Hartman, Ordinary differential equations, Wiley, Baltimore, 1973.
13. C. Hirsch, Numerical computation of internal and external flows, Vol. 1, Wiley, Chichester 1988.
14. M. Jakob, Heat transfer, Wiley, New York, 1959.
15. P. Knabner-I. Kögel-Knabner-K. U. Totsche, The modeling of reactive solute transport with sorption to mobile and immobile sorbents. Part 1: Experimental evidence and model development, Water Resources Research, 32 (1996), pp. 1611-1622.
16. S. G. Krein-J. I. Petunin-E. M. Semenov, Interpolation for linear operators, AMS Transl. Math. Monographs Vol. 54, Providence, RI, 1982.
17. C. Johnson-R. Rannacher-M. Boman, Numerics and hydrodynamics stability: Toward error control in computational fluid dynamics, SIAM J. Numer. Anal., 32 (1995), pp. 1058-1079.
18. J. L. Lions-E. Magenes, Non-homogeneous boundary problems and applications I, Springer, Berlin, 1972.
19. O. Pironneau, On the transport-diffusion algorithm and its applications to the Navier-Stokes equations, Numer. Math., 38 (1982), pp. 309-332.
20. R. Rautmann, Optimum regularity of Navier-Stokes solutions at time t=0, Math. Z., 184 (1983), pp. 141-149.
21. E. Süli, Stability and convergence of the Lagrange-Galerkin method with non-exact integration, in J. R. Whiteman (ed.): The Mathematics of Finite Elements and Applications VI, Academic Press, London, 1988, pp. 435-442.
22. H. Tanabe, Equations of evolution, Pitman, London, 1979.
23. H. Triebel, Interpolation theory, function spaces, differential operators, North-Holland, Amsterdam, 1978.
24. W. van Wahl, The equations of Navier-Stokes and abstract parabolic equations, Vieweg, Braunschweig, 1985.
25. J. Wloka, Partial differential equations, Cambridge University Press, New York, 1987.