@article{M2AN_2000__34_5_935_0, author = {Chizhonkov, Evgenii V. and Olshanskii, Maxim A.}, title = {On the domain geometry dependence of the LBB condition}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {34}, year = {2000}, pages = {935-951}, mrnumber = {1837762}, zbl = {1006.76052}, language = {en}, url = {http://dml.mathdoc.fr/item/M2AN_2000__34_5_935_0} }
Chizhonkov, Evgenii V.; Olshanskii, Maxim A. On the domain geometry dependence of the LBB condition. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 34 (2000) pp. 935-951. http://gdmltest.u-ga.fr/item/M2AN_2000__34_5_935_0/
[1] On the Constant in the LBB condition for rectangular domains. Report No 9535, Depof. Math. Univ. of Nijmegen, The Netherlands (1995). | MR 1788543
and ,[2] The finite element method with Lagrange multipliers. Numer. Math. 20(1973) 179 192. | MR 359352 | Zbl 0258.65108
,[3] On the convergence of eigenvalues formixed formulations. Ann. Sc. Norm. Sup. Pisa 25 (1997) 131 154. | Numdam | MR 1655512 | Zbl 1003.65052
, and ,[4] On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form. Math. Comp. 69(2000) 141-158. | MR 1642801 | Zbl 0938.65126
, and .[5] Finite Elemente Theorie, schnelle Loser und Anwendungen in der Elastizitatstheorie. Springer Verlag, Berlin, Heidelberg, New York (1997). | Zbl 0870.65097
,[6] A preconditioning technique for indefinite Systems resulting from mixed approximation of elliptic problems. Math. Comp. 50 (1988) 1-17. | MR 917816 | Zbl 0643.65017
and ,[7] On the existence, uniqueness and approximation of the saddle-point problems arismg from Lagrange multipliers. Numer. Math. 20 (1974) 179 192. | Numdam | Zbl 0338.90047
, (1974).[8] Mixed and hybrid finite element methods. Springer Series in Comp. Math. 15 Springer-Verlag New York (1991). | MR 1115205 | Zbl 0788.73002
and ,[9] 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 1285107 | Zbl 0821.76019
,[10] 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 483519
,[11] Some remarks on Korn's inequality. Z Angew. Math. Phys. 19 (1968) 913-920. | MR 239797 | Zbl 0169.55904
,[12] Finite element methods for Navier-Stokes equations. Springer-Verlag, Berlin (1986). | MR 851383 | Zbl 0585.65077
and ,[13] Elliptic problems in nonsmooth domains. Pitman, Boston (1985). | MR 775683 | Zbl 0695.35060
,[14] Finite element methods for viscous incompressible flows. A guide to the theory, practice and algorithms. Academic Press, London (1989). | MR 1017032
,[15] On mequahties of Korn, Friednchs and Babuska-Aziz. Arch. Ration. Mech. Anal. 40 (1971) 384-402. | Zbl 0223.73011
and ,[16] On equivalent norms. in L2 Anal. Math. No 3 (1977) 177-186. | MR 461116 | Zbl 0358.46022
,[17] On the convergence factor of Uzawa's algorithm. J. Comp. Appl. Math. 15 (1986) 191-202. | MR 846936 | Zbl 0601.76021
and ,[18] 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 415422 | Zbl 0291.35065
,[19] Stokes problem with model boundary conditions. Sbornik Mathematics 188 (1997) 603-620. | MR 1462031 | Zbl 0886.35110
,[20] On the optimal constant in the inf-sup condition for rectangle. Matematicheskie Zametki 67 (2000) 387-396. | MR 1779472 | Zbl 0979.76070
and ,[21] The Symmetrical Eigenvalue Problem Prentice-Hall, Englewood Chffs, New Jersey (1980). | MR 570116 | Zbl 0431.65017
,[22] A simple nonconforming quadrilateral Stokes element. Numer. Methods Partial Differential Equation 8 (1992) 97-111. | MR 1148797 | Zbl 0742.76051
and ,[23] Fast iterative solution of stabilized Stokes Systems part II. Using block preconditioners. SIAMJ. Numer. Anal. 31 (1994) 1352-1367. | MR 1293519 | Zbl 0810.76044
and ,[24] 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 1727107 | Zbl 0874.76070
and ,[25] An analysis of the finite element methods Prentice-Hall, New-York (1973). | MR 443377 | Zbl 0356.65096
and ,[26] Efficient solvers for incompressible flow problems. An algorithmic approach in view of computational aspects. LNCSE 6, Springer, Heidelberg (1999). | MR 1691839 | Zbl 0930.76002
,[27] FEATFLOW Finite element software for the incompressible Navier-Stokes equations. User Manual, Release 1 1 Univ of Heidelberg (1998) (http //www featflow de).
and ,