Document Zbl 0418.73068

Error estimates of finite element approximations for problems in linear elasticity. I: Problems in elastostatics. (English) Zbl 0418.73068

Arch. Ration. Mech. Anal. 72, 41-60 (1979).

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MSC:

74S05	Finite element methods applied to problems in solid mechanics
74B99	Elastic materials
74H99	Dynamical problems in solid mechanics
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74E10	Anisotropy in solid mechanics
74E05	Inhomogeneity in solid mechanics

Keywords:

error estimates; finite element approximations; linear elasticity; elastostatics; partial differential equations; inhomogeneous anisotropic linearly elastic material body; stored energy function; total energy function; piecewise polynomials; mixed problem; regular solution

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References:

[1]	Tong, P., & T. Pian, The convergence of the finite element method in solving linear elastic problems, I · Zbl 0149.42802 · doi:10.1016/0020-7683(67)90059-5
[2]	Key, S.W., A convergence investigation of the direct stiffness method, Ph. D. thesis, University of Washington 1966.
[3]	Johnson, M.W., & R.W. McLay, Convergence of the finite element method in the theory of el · Zbl 0164.26101 · doi:10.1115/1.3601191
[4]	Carlson, R.E., & C.A. Hall, Ritz approximations to two-dimensional boundary valu · Zbl 0213.17002 · doi:10.1007/BF01436326
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[10]	Fichera, G., Linear Elliptic Differential Systems and Eigenvalue Problems, Lecture Notes Series Vol. 8,Springer 1972. · Zbl 0138.36104
[11]	Fichera, G., Existence Theorems in Elasticity, in Handbuch der Physik, Band VIa/2, edited by C. Truesdell, Springer 1972.
[12]	Ciarlet, P.G., & P.A. Raviart, General Lagrange and Herm · Zbl 0243.41004 · doi:10.1007/BF00252458
[13]	Strang, G., Approximation in the finite elem · Zbl 0221.65174 · doi:10.1007/BF01395933
[14]	Nitsche, J., Ein Kriterium für die Quasi-Optimalität des Ritzschen · Zbl 0175.45801 · doi:10.1007/BF02166687
[15]	Chou, S.-I, Galerkin approximations on linear elastostatics, elastodynamics, and thermoelastodynamics, Ph. D. thesis, Rice University 1972.

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