Superconvergence and an error estimator for the finite element analysis of beams and frames (Q2712974)

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 finite element solutions and descries an posteriori error estimators of 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 using quadratics (instead of linears) for the compression and twisting terms and, as usual, cubics for the bending terms.