Estimates for deviations from exact solutions to plane problems in the cosserat theory of elasticity

A functional a posteriori estimate is obtained for control of the accuracy of approximate solutions to plane problems arising in the Cosserat theory of elasticity. We deal with the case where displacements and independent rotation are given on the boundary of the domain, a continuous medium is isotropic, and there is a linear dependence between stresses and strains. The proposed method is based on the duality theory of Calculus of Variations and can be also applied to the case of anisotropic media.