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Adaptive finite element methods for the identification of distributed parameters in elliptic equation

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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.

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Authors and Affiliations

  1. CIPR- Centre for Integrated Petroleum Research, University of Bergen, Realfagbygget, Allégaten 41, N-5007, Bergen, Norway

    Tao Feng

  2. Institute of System Science, Academy of Mathematics and System Sciences, Academia Sinica, Beijing, 100080, People’s Republic of China

    Ningning Yan

  3. Institute of Mathematics and Statistics, University of Kent, Canterbury, CT2 7NF, England

    Wenbin Liu

Authors
  1. Tao Feng
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  2. Ningning Yan
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  3. Wenbin Liu
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Correspondence to Tao Feng.

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Communicated by A. Zhou.

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Feng, T., Yan, N. & Liu, W. Adaptive finite element methods for the identification of distributed parameters in elliptic equation. Adv Comput Math 29, 27–53 (2008). https://doi.org/10.1007/s10444-007-9035-6

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  • DOI: https://doi.org/10.1007/s10444-007-9035-6

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