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A posteriori error estimation and adaptivity for linear elasticity using the reciprocal theorem. (English) Zbl 0947.74062

Summary: The reciprocal theorem of Betti and Rayleigh or in other notions duality arguments are used to derive error estimators for the finite element approximation of various quantities, including local variables like single displacements and stresses. The proposed error estimator is evaluated solving the set of equations for an additional right-hand side, by applying the energy norm error estimators two times. Furthermore, a general \(h\)-adaptive algorithm is introduced which allows us to optimize meshes with respect to different user-specified variables. The efficiency of the approach is demonstrated for plates and shells.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
74K25 Shells
74K20 Plates
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