An analysis of the p-version of the finite element method for nearly incompressible materials. Uniformly valid, optimal error estimates. (English) Zbl 0504.65061


65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
74S05 Finite element methods applied to problems in solid mechanics
Full Text: DOI EuDML


[1] Agmon, S., Douglis, A., Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II. CPAM17, 35-92 (1964) · Zbl 0123.28706
[2] Arnold, D.N.: Discretization by finite elements of a model parameter dependent problem. Numer. Math.37, 405-421 (1981) · Zbl 0446.73066
[3] Babuska, I.: Error-bounds for finite element method. Number. Math.16, 322-333 (1971) · Zbl 0214.42001
[4] Babuska, I., Aziz, A.K.: Survey Lectures. In: The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations. (ed.) Aziz, A.K., Academic Press, 1972
[5] Babuska, I., Dorr, M.: Error estimates for the combinedh andp versions of the finite element method. Numer. Math.37, 257-277 (1981) · Zbl 0487.65058
[6] Babuska, I., Szabo, B.A.: On the rates of convergence of the finite element method. Report WU/CCM-80/2, Washington University, St. Louis. Internat. J. Numer. Meth. Engng. (To appear)
[7] Babuska, I., Szabo, B.A., Katz, I.N.: Thep-version of the finite element method. SIAM J. Numer. Anal.18, 515-545 (1981) · Zbl 0487.65059
[8] Bergh, J., Löfström, J.: Interpolation Spaces. Berlin, Heidelberg, New York: Springer 1976 · Zbl 0344.46071
[9] Duvaut, G., Lions, J.L.: Inequalities in Mechanics and Physics. Berlin, Heidelberg, New York: Springer 1976 · Zbl 0331.35002
[10] Fried, I.: Shear inC 0 andC 1 bending finite elements. Int. J. Solids Structures9, 449-460 (1973)
[11] Johnson, C., Pitkäranta, J.: Analysis of some mixed finite element methods related to reduced integration. (Preprint) · Zbl 0482.65058
[12] Lions, J.L., Magenes, E.: Nonhomogeneous Boundary Value Problems and Applications, I. Berlin, Heidelberg, New York: Springer 1972 · Zbl 0223.35039
[13] Malkus, D.S., Hughes, T.J.R.: Mixed finite element methods?reduced and selective integration techniques: a unification of concepts. Comput. Appl. Mech. Engng.15, 63-81 (1978) · Zbl 0381.73075
[14] Szabo, B.A., Basu, P.K., Dunavant, D.A., Vasilopoulos, D.: Adaptive finite element technology in integrated design and analysis. Report WU/CCM-81/1. St. Louis: Washington University
[15] Vogelius, M.: A right-inverse for the divergence operator in spaces of piecewise polynomials. Application to thep-version of the finite element method. Numer. Math.41, 19-37 (1983) · Zbl 0504.65060
[16] Zienkiewcss, O.C.: The Finite Element Method in Engineering Science. McGraw-Hill, 1971
[17] Zienkiewics, O.C., Taylor, R.L., Too, J.M.: Reduced integration techniques in general analysis of plates and shells. Internat. J. Numer. Meth. Engng.5, 275-290 (1971) · Zbl 0253.73048
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.