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Adaptive finite element methods for the identification of distributed parameters in elliptic equation |
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| Authors: | Tao Feng Ningning Yan Wenbin Liu |
| Institution: | (1) CIPR- Centre for Integrated Petroleum Research, University of Bergen, Realfagbygget, Allégaten 41, N-5007 Bergen, Norway;(2) Institute of System Science, Academy of Mathematics and System Sciences, Academia Sinica, Beijing, 100080, People’s Republic of China;(3) Institute of Mathematics and Statistics, University of Kent, Canterbury, CT2 7NF, England |
| Abstract: | In this paper, adaptive finite element method is developed for the estimation of distributed parameter in elliptic equation. Both upper and lower error bound are derived and used to improve the accuracy by appropriate mesh refinement. An efficient preconditioned project gradient algorithm is employed to solve the nonlinear least-squares problem arising in the context of parameter identification problem. The efficiency of our error estimators is demonstrated by some numerical experiments. |
| Keywords: | Parameter identification Finite element approximation Adaptive finite element methods Least-squares Gauss– Newton |
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