Superconvergence and an error estimator for the finite element analysis of beams and frames

In the context of the equilibrium equations governing an Euler-Bernoulli beam and an assembly of such beams in a frame structure, this article considers the superconvergence of various parameters at various points of the finite element solutions and describes an a posteriori error estimator of the Bank Weiser type. The error estimator is shown to be consistent with the energy norm in all cases and, in the superconvergent cases that we consider, it is also shown to be asymptotically exact. As shown, asymptotic exactness can be obtained by merely using quadratics (instead of linears) for the compression and twisting terms and, as usual, cubics for the bending terms. (C) 2001 John Wiley & Sons, Inc.