A-posteriori modeling error estimation for hierarchic plate models

Summary.Hierarchic plate models are dimensional reductions obtained by semidiscretization of the three-dimensional plate problem in the transverse direction and energy projection. We derive computable a-posteriori estimators for the modeling error thus incurred under the assumption that the resulting two-dimensional plate models are solved exactly. The estimators are valid for homogeneous, monoclinic materials, for plates with unsmooth midsurfaces and for a wide class of variational edge conditions. Computable a-posteriori bounds on the effectivity indices are also derived and sufficient conditions for the asymptotic (i.e. as the plate thickness tends to zero) and the spectral (i.e. as the order of the plate model tends to infinity) exactness of the estimators are given. Numerical examples are presented.

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