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A simple error estimator and adaptive procedure for practical engineering analysis. (English) Zbl 0602.73063
A new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes. The estimator allows the global energy norm error to be well estimated and also gives a good evaluation of local errors. It can thus be combined with a full adaptive process of refinement or, more simply, provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials. When combined with an automatic mesh generator a very efficient guidance process to analysis is available. Estimates other than the energy norm have successfully been applied giving, for instance, a predetermined accuracy of stresses.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
65N15 Error bounds for boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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[1] Babuska, S I A M J. Num. Analysis 15 (1978)
[2] Babuska, Comp. Meth. Appl. Mech. Eng. 17/18 pp 519– (1979)
[3] , , and , ’Adaptive approximations in finite element structural analysis’, I S M E S, Bergamo, Italy, 1978.
[4] , and , ’Hierarchical finite element approaches, error estimates and adaptive refinement’, in (ed.), Mathematics of Finite Elements and Applications (IV). Academic Press, 1982, pp. 313-346.
[5] Zienkiewicz, Computers & Structures 16 pp 53– (1983)
[6] Kelly, Int. j. numer. methods eng. 19 pp 1593– (1983)
[7] Gago, Int. j. numer. methods eng. 19 pp 1621– (1983)
[8] and , ’A posteriori error estimation and adaptive mesh refinement in finite element method’, in (ed.) The Mathematical Basis of Finite Element Methods, Clarendon Press, Oxford, 1984.
[9] and , ’A posteriori error estimation, adaptive mesh refinement and multi-grid methods using hierarchical finite element bases’, in Mathematics of finite Elements and Applications (V), Academic Press, 1985, pp. 587-594. · doi:10.1016/B978-0-12-747255-3.50049-6
[10] , and (eds), Accuracy Estimates and Adaptive Refinement in Finite Element Computations, Wiley, 1986.
[11] The Finite Element Method, 3rd edn, McGraw-Hill, 1977.
[12] , ’Optimisation of finite element solutions’, Proc. 3rd Conf. Matrix Methods in Structural Analysis, Wright-Patterson A. F. Base, Ohio, 1971.
[13] Babuska, Math. Comp. 30 (1979)
[14] Zienkiewicz, Comp. Meth. Appl. Mech. Eng. 51 pp 3– (1985)
[15] Zienkiewicz, Communications in Applied Numerical Methods 1 pp 3– (1985)
[16] Tong, A.I.A.A.J. 7 pp 179– (1969)
[17] Private communication, 1985.
[18] , and , ’Adaptive analysis refinement and shape optimization; some new possibilities’, Int. Symp. on ’The Optimum Shape’, General Motors, September 1985.
[19] , and , ’Adaptive remeshing for compressible flow computations’, Inst. Num. Meth in Eng., University College, Swansea, CR/R/544/86, 1986 (to be published).
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