Zhu, J. Z.; Zienkiewicz, O. C. Adaptive techniques in the finite element method. (English) Zbl 0633.73070 Commun. Appl. Numer. Methods 4, No. 2, 197-204 (1988). An effective h-version finite element adaptive strategy combined with mesh regeneration is presented. This is based on the error estimator developed by the authors in Int. J. Numer. Methods Eng. 24, 337-357 (1987; Zbl 0602.73063). The rate of convergence of the adaptive procedure has been tested for some examples and very strong convergence observed. Unlike some existing h-version adaptive procedures, a nearly optimal mesh of predicted accuracy can be obtained in one or two adaptive process steps. Cited in 1 ReviewCited in 55 Documents MSC: 74S05 Finite element methods applied to problems in solid mechanics 65N15 Error bounds for boundary value problems involving PDEs 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs Keywords:elliptic problem; effective h-version finite element adaptive strategy; mesh regeneration; rate of convergence Citations:Zbl 0623.65120; Zbl 0602.73063 PDFBibTeX XMLCite \textit{J. Z. Zhu} and \textit{O. C. Zienkiewicz}, Commun. Appl. Numer. Methods 4, No. 2, 197--204 (1988; Zbl 0633.73070) Full Text: DOI References: [1] Zienkiewicz, Int. j. numer. methods eng. 24 pp 337– (1987) [2] Babuska, SIAM J. Num. Anal. 15 pp 736– (1978) [3] Babuska, Comp. Meth. Appl. Mech. Eng. 17/18 pp 519– (1979) [4] Zienkiewicz, Comp. Struct. 16 pp 53– (1983) [5] Kelly, Int. j. numer. methods eng. 19 pp 1593– (1983) [6] Gago, Int. j. numer. methods eng. 19 pp 1621– (1983) [7] and . ’A posteriori error estimation, adaptive mesh refinement and multi-grid methods using hierarchical finite element bases’, In Mathematics of Finite elements and Applications, vol. V. (Ed. ), Academic Press, New York, 1985, pp. 587-594. [8] , and (Eds.), Accuracy Estimates and Adaptive Refinement in Finite Element Computations, Wiley, New York, 1986. [9] Rank, Commun. appl. num. methods 3 pp 243– (1987) [10] ’Error estimation, adaptivity and multigrid techniques in the finite element method’, Ph.D. thesis, Univ. of Wales, Swansea, U.K. (Feb. 1987). [11] and . ’Computation of the amplitude of stress singular terms for cracks and re-entrant corners’, Report WU/CCM-86/1. Center for Computational Mechanics, Washington Univ. (1986). [12] , and , ’Adaptive remeshing for compressible flow computations’, J. Comp. Phys. (to be published). · Zbl 0631.76085 [13] Baehmann, Int. j. numer. methods eng. 24 pp 1043– (1987) [14] ’Estimation and control of error based on p-convergence’, in Accuracy Estimates and Adaptivity for Finite Elements, (Eds. et al), Wiley, New York, 1986, pp. 61-78. 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.