On the domain geometry dependence of the LBB condition
Evgenii V. Chizhonkov; Maxim A. Olshanskii
- Volume: 34, Issue: 5, page 935-951
- ISSN: 0764-583X
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topChizhonkov, Evgenii V., and Olshanskii, Maxim A.. "On the domain geometry dependence of the LBB condition." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 34.5 (2000): 935-951. <http://eudml.org/doc/194026>.
@article{Chizhonkov2000,
author = {Chizhonkov, Evgenii V., Olshanskii, Maxim A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {domain geometry dependence; LBB condition; finite element velocity-pressure pair; mesh-independent limit; Nečas inequality},
language = {eng},
number = {5},
pages = {935-951},
publisher = {Dunod},
title = {On the domain geometry dependence of the LBB condition},
url = {http://eudml.org/doc/194026},
volume = {34},
year = {2000},
}
TY - JOUR
AU - Chizhonkov, Evgenii V.
AU - Olshanskii, Maxim A.
TI - On the domain geometry dependence of the LBB condition
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2000
PB - Dunod
VL - 34
IS - 5
SP - 935
EP - 951
LA - eng
KW - domain geometry dependence; LBB condition; finite element velocity-pressure pair; mesh-independent limit; Nečas inequality
UR - http://eudml.org/doc/194026
ER -
References
top- [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). Zbl0871.76051MR1788543
- [2] I. Babuška, The finite element method with Lagrange multipliers. Numer. Math. 20(1973) 179 192. Zbl0258.65108MR359352
- [3] D. Boffi, F. Brezzi and L. Gastaldi, On the convergence of eigenvalues formixed formulations. Ann. Sc. Norm. Sup. Pisa 25 (1997) 131 154. Zbl1003.65052MR1655512
- [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. Zbl0938.65126MR1642801
- [5] D. Braess, Finite Elemente Theorie, schnelle Loser und Anwendungen in der Elastizitatstheorie. Springer Verlag, Berlin, Heidelberg, New York (1997). Zbl0870.65097
- [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. Zbl0643.65017MR917816
- [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. Zbl0338.90047
- [8] F. Brezzi and M. Fortin, Mixed and hybrid finite element methods. Springer Series in Comp. Math. 15 Springer-Verlag New York (1991). Zbl0788.73002MR1115205
- [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. Zbl0821.76019MR1285107
- [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.
- [11] C.M. Dafermos, Some remarks on Korn's inequality. Z Angew. Math. Phys. 19 (1968) 913-920. Zbl0169.55904MR239797
- [12] V. Girault and P.A. Raviart, Finite element methods for Navier-Stokes equations. Springer-Verlag, Berlin (1986). Zbl0585.65077MR851383
- [13] P. Grisvard, Elliptic problems in nonsmooth domains. Pitman, Boston (1985). Zbl0695.35060MR775683
- [14] M. Gunsburger, Finite element methods for viscous incompressible flows. A guide to the theory, practice and algorithms. Academic Press, London (1989). MR1017032
- [15] C.O. Horgan and L.E. Payne, On mequahties of Korn, Friednchs and Babuska-Aziz. Arch. Ration. Mech. Anal. 40 (1971) 384-402. Zbl0223.73011
- [16] G. M. Kobelkov, On equivalent norms. in L2 Anal. Math. No 3 (1977) 177-186. Zbl0358.46022
- [17] U. Langer and W. Queck, On the convergence factor of Uzawa's algorithm. J. Comp. Appl. Math. 15 (1986) 191-202. Zbl0601.76021MR846936
- [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. Zbl0291.35065
- [19] M. A. Olshanskii, Stokes problem with model boundary conditions. Sbornik Mathematics 188 (1997) 603-620. Zbl0886.35110MR1462031
- [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. Zbl0979.76070MR1779472
- [21] B.N. Parlett, The Symmetrical Eigenvalue Problem Prentice-Hall, Englewood Chffs, New Jersey (1980). Zbl0431.65017MR570116
- [22] R. Rannacher and S. Turek, A simple nonconforming quadrilateral Stokes element. Numer. Methods Partial Differential Equation 8 (1992) 97-111. Zbl0742.76051MR1148797
- [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. Zbl0810.76044MR1293519
- [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. Zbl0874.76070
- [25] G. Strang and G.I. Fix, An analysis of the finite element methods Prentice-Hall, New-York (1973). Zbl0356.65096MR443377
- [26] S. Turek, Efficient solvers for incompressible flow problems. An algorithmic approach in view of computational aspects. LNCSE 6, Springer, Heidelberg (1999). Zbl0930.76002MR1691839
- [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).
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