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Int. J. Numer. Anal. Mod., 6 (2009), pp. 17-32. |
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Adaptive finite element methods for parameter estimation problems in linear elasticity Tao Feng 1, Marten Gulliksson 2, Wenbin Liu 3 1 CIPR, University of Bergen, P.O. Box 7800, N-5020 Bergen, Norway.2 Department of Engineering, Physics and Mathematics, Mid Sweden Univ., SE-851 70 Sundsvall, Sweden. 3 Institute of Mathematics and Statistics, University of Kent, Canterbury, CT2 7NF, England. Received by the editors November 28, 2007 and, in revised form, December 22, 2007. Abstract
In this paper, the Lame coefficients in the linear elasticity problem are estimated by using the measurements of displacement. Some a posteriori error estimators for the approximation error of the parameters are derived, and then adaptive finite element schemes are developed for the discretization of the parameter estimation problem, based on the error estimators. The Gauss-Newton method is employed to solve the discretized nonlinear least-squares problem. Some numerical results are presented. AMS subject classifications: 65N30, 49J20, 74B05, 65M32 Key words: Parameter estimation, finite element approximation, adaptive finite element methods, a posteriori error estimates, linear elasticity. Email: tao.feng@cipr.uib.no, marten.gulliksson@miun.se, w.b.liu@kent.ac.uk |