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Superconvergence and an error estimator for the finite element analysis of beams and frames
Author(s) -
Kirby J. A.,
Warby M. K.,
Whiteman J. R.
Publication year - 2001
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/1098-2426(200103)17:2<169::aid-num6>3.0.co;2-m
Subject(s) - superconvergence , mathematics , estimator , finite element method , context (archaeology) , a priori and a posteriori , norm (philosophy) , partial differential equation , bernoulli's principle , partial derivative , mathematical analysis , structural engineering , statistics , political science , law , engineering , paleontology , philosophy , epistemology , biology , aerospace engineering
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. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 169–197, 2001