The usual and not controlled discretization is a source of unacceptable numerical errors or erroneous solutions in finite element analysis. These effects can significantly reduce the possibility of adequate numerical representation of real objects, especially in nonlinear analysis of, for example, complex shell structures. In these circumstances, an adaptive arrangement of computations is a powerful solution technique becoming increasingly popular among researchers and engineers. The crucial part of this technique is the adequacy analysis where the errors have to be economically quantified and estimate.

In this study, a new general error estimation procedure which includes the control of both physical and geometrical fields in adaptative analysis is presented. The control procedures are based on superconvergent properties of certain points in a finite element model, local linearisation and geometrical interpretation for different discrete fields under consideration. Local a posteriori estimates of the errors follow directly from the finite element analysis without additional computations such as, for example, stress smoothing or residual computations. The linear and nonlinear analysis with the proposed scheme can be performed. Some simple examples demonstrate practical applicability and efficiency of the new description.

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