Liberman, Elsa A posteriori error estimator for a mixed finite element method for Reissner-Mindlin plate. (English) Zbl 1017.74066 Math. Comput. 70, No. 236, 1383-1396 (2001). Summary: We present an a posteriori error estimator for a mixed finite element method for the Reissner-Mindlin plate model. The finite element method we deal with, was analyzed by R. Durán and E. Liberman [Math. Comput. 58, 561-573 (1992; Zbl 0763.73054)] and can also be seen as a particular example of the general family analyzed by F. Brezzi, M. Fortin and R. Stenberg [Math. Models Methods Appl. Sci. 1, No. 2, 125-151 (1991; Zbl 0751.73053)]. The estimator is based on the evaluation of the residual of finite element solution. We show that the estimator yields local lower and global upper bounds on the error in a natural norm for the problem, which includes \(H^1\) norms of the terms corresponding to deflection and rotation, and a dual norm for the shearing force. The estimates are valid uniformly with respect to plate thickness. Cited in 6 Documents MSC: 74S05 Finite element methods applied to problems in solid mechanics 74K20 Plates 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs Keywords:a posteriori error estimate; mixed finite element method; Reissner-Mindlin plate model; deflection; rotation; dual norm; shearing force; H(1)-norm; local lower error bound; global upper error bound Citations:Zbl 0763.73054; Zbl 0751.73053 × Cite Format Result Cite Review PDF Full Text: DOI Link References: [1] D. N. Arnold and F. Brezzi, Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates, RAIRO Modél. Math. Anal. Numér. 19 (1985), no. 1, 7 – 32 (English, with French summary). · Zbl 0567.65078 [2] Douglas N. Arnold and Richard S. 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