Optimal error estimates for the Stokes and Navier-Stokes equations with slip-boundary condition
ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 5, pp. 923-938. 
@article{M2AN_1999__33_5_923_0,
     author = {B\"ansch, Eberhard and Deckelnick, Klaus},
     title = {Optimal error estimates for the {Stokes} and {Navier-Stokes} equations with slip-boundary condition},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {923--938},
     publisher = {EDP-Sciences},
     volume = {33},
     number = {5},
     year = {1999},
     mrnumber = {1726716},
     zbl = {0948.76035},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1999__33_5_923_0/}
}
TY  - JOUR
AU  - Bänsch, Eberhard
AU  - Deckelnick, Klaus
TI  - Optimal error estimates for the Stokes and Navier-Stokes equations with slip-boundary condition
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1999
SP  - 923
EP  - 938
VL  - 33
IS  - 5
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/M2AN_1999__33_5_923_0/
LA  - en
ID  - M2AN_1999__33_5_923_0
ER  - 
%0 Journal Article
%A Bänsch, Eberhard
%A Deckelnick, Klaus
%T Optimal error estimates for the Stokes and Navier-Stokes equations with slip-boundary condition
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1999
%P 923-938
%V 33
%N 5
%I EDP-Sciences
%U http://www.numdam.org/item/M2AN_1999__33_5_923_0/
%G en
%F M2AN_1999__33_5_923_0
Bänsch, Eberhard; Deckelnick, Klaus. Optimal error estimates for the Stokes and Navier-Stokes equations with slip-boundary condition. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 5, pp. 923-938. http://www.numdam.org/item/M2AN_1999__33_5_923_0/

[1] E. Bänsch, Local Mesh Refinement in 2 and 3 Dimensions. Impact Comp. Sci. Eng. 3 (1991) 181-191. | MR | Zbl

[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). | MR | Zbl

[3] G. K. Batchelor, An Introduction to Fluid Dynamics. University Press, Cambridge (1970). | MR | Zbl

[4] C. Bernardi, Optimal finite element interpolation on curved domains. SIAM J. Numer. Anal. 26 (1989) 212-234. | MR | Zbl

[5] F. Brezzi and M. Fortin, Mixed and hybrid finite element methods. Springer, New York (1991). | MR | Zbl

[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. | MR

[7] P. G. Ciarlet, The finite element method for elliptic problems. North-Holland, Amsterdam (1977). | MR | Zbl

[8] K. Deimling, Nonlinear Functional Analysis. Springer, Berlin (1985). | MR | Zbl

[9] V. Girault and P. A. Raviart, Finite element methods for Navier-Stokes equations, Theory and Algorithms. Springer, Berlin (1986). | MR | Zbl

[10] C. Cuvelier and J. M. Driessen, Thermocapillary free boundaries in crystal growth. J. Fluid Mech. 169 (1986) 1-26. | Zbl

[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. | Zbl

[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). | MR | Zbl

[13] M. Lenoir, Optimal isoparametric finite elements and error estimates for domains involving curved boundaries. SIAM J. Numer. Anal. 23 (1986) 562-580. | MR | Zbl

[14] J. A. Nitsche, On Korn's second inequality. RAIRO Anal. Numér. 15 (1981) 237-248. | Numdam | MR | Zbl

[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. | Zbl

[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. | MR | Zbl

[19] R. Verfürth, A combined conjugate gradient-multigrid algorithm for the numerical solutin of the Stokes problem. IMA J. Numer. Anal. 4 (1984) 441-455. | MR | Zbl

[20] R. Verfürth, Finite element approximation of steady Navier-Stokes equations with mixed boundary conditions. Math. Modelling Numer. Anal. 19 (1985) 461-475. | Numdam | MR | Zbl

[21] R. Verfürth, Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition. Numer. Math. 50 (1987) 697-721. | MR | Zbl

[22] R. Verfürth, Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition II. Numer. Math. 59 (1991) 615-636. | MR | Zbl