Optimal error estimates for the stokes and Navier-Stokes equations with slip-boundary condition

Mathematical Modelling and Numerical Analysis

Volumn 33, Issue 5, 1999, Pages 923-938

  Bänsch, Eberhard ^a   Deckelnick, Klaus ^b  

^a UNIVERSITY OF BREMEN   (Germany)

^b UNIVERSITY OF SUSSEX   (United Kingdom)

Author keywords

Error estimates; Finite elements; Navier Stokes equations; Slip boundary condition; Stokes equations

Indexed keywords

EID: 0040944113     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:1999126     Document Type: Article

References (22)

1. E. Bänsch, Local Mesh Refinement in 2 and 3 Dimensions. Impact Comp. Sci. Eng. 3 (1991) 181-191.
2. E. Bänsch and B. Höhn, Numerical treatment of the Navier-Stokes equations with slip-boundary conditions. Preprint 9/1998, Universität Freiburg; SIAM J. Sci. Comp. (submitted).
3. G.K. Batchelor, An Introduction to Fluid Dynamics. University Press, Cambridge (1970).
4. C. Bernardi, Optimal finite element interpolation on curved domains. SIAM J. Numer. Anal. 26 (1989) 212-234.
5. F. Brezzi and M. Fortin, Mixed and hybrid finite element methods. Springer, New York (1991).
6. M.O. Bristeau, R. Glowinski and J. Periaux, Numerical methods for the Navier-Stokes equations. Application to the simulation of compressible and incompressible flows. Comput. Phys. Rep. 6 (1987) 73-188.
7. P.G. Ciarlet, The finite element method for elliptic problems. North-Holland, Amsterdam (1977).
8. K. Deimling, Nonlinear Functional Analysis. Springer, Berlin (1985).
9. V. Girault and P.A. Raviart, Finite element methods for Navier-Stokes equations, Theory and Algorithms. Springer, Berlin (1986).
10. C. Cuvelier and J.M. Driessen, Thermocapillary free boundaries in crystal growth. J. Fluid Mech. 169 (1986) 1-26.
11. S.F. Kistler and L.E. Scriven, Coating flow theory by finite element and asymptotic analysis of the Navier-Stokes system. Internat. J. Numer. Methods Fluids 4 (1984) 207-229.
12. P. Knobloch, Variational Crimes in a Finite Element Discretization of 3D Stokes Equations with Nonstandard Boundary Conditions. Preprint MBI-97-4, University of Magdeburg (1997).
13. M. Lenoir, Optimal isoparametric finite elements and error estimates for domains involving curved boundaries. SIAM J. Numer. Anal. 23 (1986) 562-580.
14. J.A. Nitsche, On Korn's second inequality. RAIRO Anal. Numér. 15 (1981) 237-248.
15. F. Otto, Die Babuška-Brezzi Bedingung für das Taylor-Hood-Element. Diploma thesis, University of Bonn, Germany (1990).
16. H. Saito and L.E Scriven, Study of Coating Flow by the Finite Element Method. J. Comput. Phys. 42 (1981) 53-76.
17. D. Schwabe, Surface-Tension-Driven Flow in Crystal Growth Melts, in Crystal Growth, Properties and Applications 11. Springer, Berlin (1988).
18. S.A. Solonnikov and V.E. Ščadilov, On a boundary value problem for a stationary system of Navier-Stokes equations. Proc. Steklov Inst. Math. 125 (1973) 186-199.
19. R. Verfürth, A combined conjugate gradient-multigrid algorithm for the numerical solution of the Stokes problem. IMA J. Numer. Anal. 4 (1984) 441-455.
20. R. Verfürth, Finite element approximation of steady Navier-Stokes equations with mixed boundary conditions. Math. Modelling Numer. Anal 19 (1985) 461-475.
21. R. Verfürth, Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition. Numer. Math. 50 (1987) 697-721.
22. R. Verfürth, Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition II. Numer. Math. 59 (1991) 615-636.