TY - JOUR T1 - Adaptive Finite Element Methods for Parameter Estimation Problems in Linear Elasticity JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 17 EP - 32 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/754.html KW - Parameter estimation, finite element approximation, adaptive finite element methods, a posteriori error estimates, linear elasticity. AB -

In this paper, the Lamé 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.