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Volume 6, Issue 1
Adaptive Finite Element Methods for Parameter Estimation Problems in Linear Elasticity

T. Feng, M. Gulliksson & W. Liu

Int. J. Numer. Anal. Mod., 6 (2009), pp. 17-32.

Published online: 2009-06

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  • Abstract

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.

  • Keywords

Parameter estimation, finite element approximation, adaptive finite element methods, a posteriori error estimates, linear elasticity.

  • AMS Subject Headings

65N30, 49J20, 74B05, 65M32

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-6-17, author = {T. Feng, M. Gulliksson and W. Liu}, title = {Adaptive Finite Element Methods for Parameter Estimation Problems in Linear Elasticity}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2009}, volume = {6}, number = {1}, pages = {17--32}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/754.html} }
TY - JOUR T1 - Adaptive Finite Element Methods for Parameter Estimation Problems in Linear Elasticity AU - T. Feng, M. Gulliksson & W. Liu 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.

T. Feng, M. Gulliksson and W. Liu. (2009). Adaptive Finite Element Methods for Parameter Estimation Problems in Linear Elasticity. International Journal of Numerical Analysis and Modeling. 6 (1). 17-32. doi:
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