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On the approximation of the spectrum of the Stokes operator. (English) Zbl 0683.65095
The Stokes problem is considered in a bounded domain. It is proved that there exists an infinite sequence of eigenvalues and a corresponding sequence of eigenfunctions of the Stokes operator. Error estimates are derived for the approximate calculation of the eigenvalues of the Stokes operator. These estimates are valid for the regularized version of mixed methods which are used for the approximate solution of the Stokes problem.
Reviewer: Z.D.zygadło
MSC:
65N25Numerical methods for eigenvalue problems (BVP of PDE)
65N15Error bounds (BVP of PDE)
76D07Stokes and related (Oseen, etc.) flows
35P15Estimation of eigenvalues and upper and lower bounds for PD operators
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Full Text: EuDML
References:
[1] K. J. BATHE, Finite Element Procedures in Engineering Analysis, Prentice-Hall, 1982, Englewood Cliffs, N.J. · Zbl 0528.65053
[2] [2] M. BERCOVIER, Perturbation of mixed variational problems : Application to mixed finite element methods, R.A.I.R.O. Anal. Num. 12 (1978), 211-236. Zbl0428.65059 MR509973 · Zbl 0428.65059 · eudml:193320
[3] [3] C. CANUTO, Eigenvalue approximation by mixed methods, R.A.I.R.O. Anal. Num. 12 (1978), 25-50. Zbl0434.65032 MR488712 · Zbl 0434.65032 · eudml:193309
[4] [4] C. CANUTO, A hybrid finite element to compute the free vibration frequencies of a clamped plate, R.A.I.R.O. Anal. Num. 15 (1981), 101-118. Zbl0462.73049 MR618818 · Zbl 0462.73049 · eudml:193371
[5] V. GIRAULT and P.-A. RAVIART, Finite Element Approximation of the Navier-Stokes Equations, Lecture Notes in Mathematics 749, Springer-Verlag, 1979, New York, Heidelberg, Berlin. Zbl0413.65081 MR548867 · Zbl 0413.65081 · doi:10.1007/BFb0063447
[6] D. F. GRIFFITHS, Finite elements for incompressible flow, Math. Meth. in the Appl. Sci. 1 (1979), 16-31. Zbl0425.65061 MR548403 · Zbl 0425.65061 · doi:10.1002/mma.1670010103
[7] D. F. GRIFFITHS, An approximately divergence-free 9-node velocity element (with variations) for incompressible flows, Int. J. Num. Meth. Fluids 1 (1981), 323-346. Zbl0469.76026 MR633811 · Zbl 0469.76026 · doi:10.1002/fld.1650010405
[8] B. MERCIER, J. OSBORN, J. RAPPAZ and P.-A. RAVIART, Eigenvalue approximation of mixed and hybrid methods, Math. Compt. 36 (1981), 427-453. Zbl0472.65080 MR606505 · Zbl 0472.65080 · doi:10.2307/2007651
[9] J. T. ODEN, N. KIKUCHI and Y. J. SONG, Penalty-finite element methods for the analysis of Stokesian flows, Comp. Meth. Appl. Mech. Eng. 31 (1982), 297-239. Zbl0478.76041 MR677872 · Zbl 0478.76041 · doi:10.1016/0045-7825(82)90010-X
[10] J. S. PETERSON, An application of mixed finite element methods to the stability of the incompressible Navier-Stokes equations, SIAM J. Sci. Stat. Comput. 4 (1983), 626-634. Zbl0526.76039 MR725657 · Zbl 0526.76039 · doi:10.1137/0904043
[11] G. STRANG and G. F. FIX, An Analysis of the Finite Element Method, Prentice-Hall, 1973, Englewood Cliffs, N.J. Zbl0356.65096 MR443377 · Zbl 0356.65096
[12] R. TEMAM, Navier-Stokes Equations, North-Holland, 1979, Amsterdam, New York, Oxford. Zbl0426.35003 · Zbl 0426.35003
[13] R. TEMAM, Navier-Stokes Equations and Nonlinear Functional Analysis, CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, 1983, Philadelphia. Zbl0833.35110 MR764933 · Zbl 0833.35110
[14] F. THOMASSET, Implementation of the Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, 1981, New York, Heidelberg, Berlin. Zbl0475.76036 MR720192 · Zbl 0475.76036