On the domain geometry dependence of the LBB condition
ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 5, pp. 935-951. 
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     author = {Chizhonkov, Evgenii V. and Olshanskii, Maxim A.},
     title = {On the domain geometry dependence of the {LBB} condition},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {935--951},
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     zbl = {1006.76052},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2000__34_5_935_0/}
}
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Chizhonkov, Evgenii V.; Olshanskii, Maxim A. On the domain geometry dependence of the LBB condition. ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 5, pp. 935-951. http://www.numdam.org/item/M2AN_2000__34_5_935_0/

[1] P.P. Aristov and E.V. Chizhonkov, On the Constant in the LBB condition for rectangular domains. Report No 9535, Depof. Math. Univ. of Nijmegen, The Netherlands (1995). | MR

[2] I. Babuška, The finite element method with Lagrange multipliers. Numer. Math. 20(1973) 179 192. | MR | Zbl

[3] D. Boffi, F. Brezzi and L. Gastaldi, On the convergence of eigenvalues formixed formulations. Ann. Sc. Norm. Sup. Pisa 25 (1997) 131 154. | Numdam | MR | Zbl

[4] D. Boffi, F. Brezzi and L. Gastaldi. On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form. Math. Comp. 69(2000) 141-158. | MR | Zbl

[5] D. Braess, Finite Elemente Theorie, schnelle Loser und Anwendungen in der Elastizitatstheorie. Springer Verlag, Berlin, Heidelberg, New York (1997). | Zbl

[6] J.H. Bramble and J.E. Pasciak, A preconditioning technique for indefinite Systems resulting from mixed approximation of elliptic problems. Math. Comp. 50 (1988) 1-17. | MR | Zbl

[7] F. Brezzi, (1974). On the existence, uniqueness and approximation of the saddle-point problems arismg from Lagrange multipliers. Numer. Math. 20 (1974) 179 192. | Numdam | Zbl

[8] F. Brezzi and M. Fortin, Mixed and hybrid finite element methods. Springer Series in Comp. Math. 15 Springer-Verlag New York (1991). | MR | Zbl

[9] E. V. Chizhonkov, Application of the Cossera spectrum to the optimization of a method for solving the Stokes Problem. Russ. J. Numer. Anal. Math. Model 9 (1994) 191-199. | MR | Zbl

[10] M. Crouzeix, Étude d'une méthode de linéarisation Résolution des équations de Stokes stationaires. Application aux équations des Navier - Stokes stationaires, Cahiers de l'IRIA (1974) 139-244. | MR

[11] C.M. Dafermos, Some remarks on Korn's inequality. Z Angew. Math. Phys. 19 (1968) 913-920. | MR | Zbl

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

[13] P. Grisvard, Elliptic problems in nonsmooth domains. Pitman, Boston (1985). | MR | Zbl

[14] M. Gunsburger, Finite element methods for viscous incompressible flows. A guide to the theory, practice and algorithms. Academic Press, London (1989). | MR

[15] C.O. Horgan and L.E. Payne, On mequahties of Korn, Friednchs and Babuska-Aziz. Arch. Ration. Mech. Anal. 40 (1971) 384-402. | Zbl

[16] G. M. Kobelkov, On equivalent norms. in L2 Anal. Math. No 3 (1977) 177-186. | MR | Zbl

[17] U. Langer and W. Queck, On the convergence factor of Uzawa's algorithm. J. Comp. Appl. Math. 15 (1986) 191-202. | MR | Zbl

[18] S.G. Mikhlin, The spectrum of an operator pencil of the elasticity theory. Uspekhi Mat Nauk 28 (1973) 43-82, English translation in Russian Math. Surveys, 28. | MR | Zbl

[19] M. A. Olshanskii, Stokes problem with model boundary conditions. Sbornik Mathematics 188 (1997) 603-620. | MR | Zbl

[20] M.A. Olshanskii and E.V. Chizhonkov, On the optimal constant in the inf-sup condition for rectangle. Matematicheskie Zametki 67 (2000) 387-396. | MR | Zbl

[21] B.N. Parlett, The Symmetrical Eigenvalue Problem Prentice-Hall, Englewood Chffs, New Jersey (1980). | MR | Zbl

[22] R. Rannacher and S. Turek, A simple nonconforming quadrilateral Stokes element. Numer. Methods Partial Differential Equation 8 (1992) 97-111. | MR | Zbl

[23] D. Silvester and A. Wathen, Fast iterative solution of stabilized Stokes Systems part II. Using block preconditioners. SIAMJ. Numer. Anal. 31 (1994) 1352-1367. | MR | Zbl

[24] M. Schafer and S. Turek, Benchmark computations of laminar flow around cylinder, in Flow Simulation with High-Performance Computers II, E. H. Hirschel Ed, Notes on Numerical Fluid Mechanics, 52, Vieweg (1996) 547-566. | MR | Zbl

[25] G. Strang and G.I. Fix, An analysis of the finite element methods Prentice-Hall, New-York (1973). | MR | Zbl

[26] S. Turek, Efficient solvers for incompressible flow problems. An algorithmic approach in view of computational aspects. LNCSE 6, Springer, Heidelberg (1999). | MR | Zbl

[27] S. Turek and Chr. Becker, FEATFLOW Finite element software for the incompressible Navier-Stokes equations. User Manual, Release 1 1 Univ of Heidelberg (1998) (http //www featflow de).