Malkus, D. S. Eigenproblems associated with the discrete LBB condition for incompressible finite elements. (English) Zbl 0457.73051 Int. J. Eng. Sci. 19, 1299-1310 (1981). Reviewer: H. Bufler Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 41 Documents MSC: 74S05 Finite element methods applied to problems in solid mechanics 65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs 49M29 Numerical methods involving duality 49S05 Variational principles of physics Keywords:incompressible element formulations; basic stability condition; LBB condition; mixed variational principles in incompressible media; linear elasticity; Stokes flow; discrete eigenstructure; relationship between natural mode eigenproblem and eigenproblems which determine norm of inverse of discrete operator PDFBibTeX XMLCite \textit{D. S. Malkus}, Int. J. Eng. Sci. 19, 1299--1310 (1981; Zbl 0457.73051) Full Text: DOI References: [1] Babuška, I.; Oden, J. T.; Lee, J. K., Comp. Meth. Appl. Mech. Engng, 11, 175 (1977) [2] Brezzi, F., R.A.I.R.O., 8, 129 (1974) [3] Babuška, I.; Azia, A. K., Mathematical Foundations of the Finite Element Method (1972), Academic Press: Academic Press New York [4] Fortin, M., R.A.I.R.O., 11, 342 (1977) [5] Bercovier, M., R.A.I.R.O., 12, 211 (1978) [6] HlavaČek, I.; Necas, J., Arch. Rat. Mech. Anal., 36, 305 (1970) [7] Wilkinson, J. H., The Algebraic Eigenvalue Problem (1965), Clarendon Press: Clarendon Press Oxford · Zbl 0258.65037 [8] Forsythe, G.; Moler, C., Computer Solution of Linear Algebraic Systems (1967), Prentice-Hall: Prentice-Hall New York · Zbl 0154.40401 [9] Gantmacher, F. R., Matrix Theory II (1971), New York, Chelsea · Zbl 0322.15004 [10] Moler, C.; Stewart, G. W., S.I.A.M. J. Numer. Anal., 10, 241 (1973) [11] Stewart, G. W., S.I.A.M. J. Numer. Anal., 9, 669 (1972) [12] Malkus, D. S.; Hughes, T. J.R., Comp. Meth. Appl. Mech. Engng, 15, 63 (1978) [13] Mercier, B., Int. J. Num. Meth. Engng, 14, 942 (1979) [14] Hughes, T. J.R.; Malkus, D. S., (Proc. Int. Symp. Hybrid Mixed Finite Element Methods. Proc. Int. Symp. Hybrid Mixed Finite Element Methods, Atlanta, Georgia (1981), Wiley: Wiley New York) [15] Kolata, William G., Math. Comp., 33, 145, 63 (1979) [16] Sani, R. L.; Gresho, P. M.; Lee, R. L.; Griffiths, D. F., Int. J. Num. Meth. Fluids, 1 (1981) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.