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Upper bounds of the error in local quantities using equilibrated and compatible finite element solutions for linear elastic problems. (English) Zbl 1086.74041

Summary: When local quantities are computed using the principle of virtual work, dual analysis, which provides an upper bound of the global error, may also be applied to the virtual problem. H. Greenberg [J. Math. Phys. 27, 161–182 (1948; Zbl 0031.31001)] and K. Washizu [J. Math. Phys. 32, 117–128 (1953; Zbl 0051.41004)] proposed alternative approaches to combine the global error bounds of the real and virtual problems, providing upper bounds of the local error. It is shown in this paper that optimising Greenberg’s approach corresponds to using Washizu’s approach, which, in turn, may be further improved. These approaches are used to provide finite element error indicators for adaptive refinement.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
65N15 Error bounds for boundary value problems involving PDEs
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