A posteriori error estimation and adaptivity for linear elasticity using the reciprocal theorem

Abstract

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, simply 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 current approach is demonstrated for plate and shell examples.