Babuška, Ivo; Szabo, Barna On the rates of convergence of the finite element method. (English) Zbl 0498.65050 Int. J. Numer. Methods Eng. 18, 323-341 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 50 Documents MSC: 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 Keywords:asymptotic rates of convergence; strain energy norm; finite element; mesh refinement; increasing polynomial order; comparison; model problems; shear displacement; edge crack × Cite Format Result Cite Review PDF Full Text: DOI References: [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. · doi:10.1016/B978-0-12-358503-5.50013-0 [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. · doi:10.1016/B978-0-12-068650-6.50006-X [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) 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.