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On the rates of convergence of the finite element method. (English) Zbl 0498.65050

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S05 Finite element methods applied to problems in solid mechanics
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
74R05 Brittle damage
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[1] ’Analysis of stresses and strains near the end of a crack traversing a plate’, J. Appl. Mech., ASME (1957).
[2] and , Mathematical Theory of Finite Elements, Wiley, 1976.
[3] Mathematical Theory of Elasticity, 2nd edn, McGraw-Hill, 1956, pp. 86-87.
[4] ’Stress singularities resulting from various boundary conditions in angular corners of plates in extension’, J. Appl. Mech., ASME, 526-528 (1952).
[5] ’Behavior of the solutions of an elliptic boundary value problem in a polygon or polyhedral domain’, in Numerical Solution of Partial Differential Equations, 3rd edn (Ed.), Academic Press, New York, 1976, pp. 207-274.
[6] Kondratev, Trans. Moscow Math. Soc. 16 pp 227– (1967)
[7] and , An Analysis of the Finite Element Method, Prentice-Hall, New Jersey, 1973, p. 40.
[8] and , ’Survey lectures on the mathematical foundations of the finite element method’, in Mathematical Foundations of the finite Element Method with Applications to Partial Differential Equations ( Ed.), Academic Press, New York, 1972, pp. 3-363.
[9] Widlund, Num. Math. 27 pp 327– (1977)
[10] Babuska, Num. Math. 33 pp 447– (1979)
[11] and , ’Theoretical Manual and Users’ Guide for COMET-X’, Center for Computational Mechanics, Washington Univ., St. Louis, MO (1977).
[12] Szabo, Comp. Math. Appl. 5 pp 99– (1979)
[13] and , ’Reliable error estimation and mesh adaptation for the finite element method’, in Computational Methods in Nonlinear Mechanics ( Ed.), North-Holland, Amsterdam, 1980, pp. 67-108.
[14] Babuska, SIAM J. Numer. Anal. 18 pp 515– (1981)
[15] Szabo, Int. J. num. Meth. Engng 12 pp 551– (1978)
[16] Babuska, Num. Math. 37 pp 257– (1981)
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