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Numerical identification of a Robin coefficient in parabolic problems


Authors: Bangti Jin and Xiliang Lu
Journal: Math. Comp. 81 (2012), 1369-1398
MSC (2010): Primary 65M30, 65M32, 65M12
Published electronically: January 11, 2012
MathSciNet review: 2904583
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Abstract: This paper studies a regularization approach for an inverse problem of estimating a spatially-and-temporally dependent Robin coefficient arising in the analysis of convective heat transfer. The parameter-to-state map is analyzed, especially a differentiability result is established. A regularization approach is proposed, and the properties, e.g., existence and optimality system, of the functional are investigated. A finite element method is adopted for discretizing the continuous optimization problem, and the convergence of the finite element approximations as the mesh size and temporal step size tend to zero is established. Numerical results by the conjugate gradient method for one- and two-dimensional problems are presented.


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Additional Information

Bangti Jin
Affiliation: Department of Mathematics and Institute for Applied Mathematics and Computational Science, Texas A&M University, College Station, Texas 77843-3368
Email: btjin@math.tamu.edu

Xiliang Lu
Affiliation: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, People’s Republic of China
Email: xllv.math@whu.edu.cn

DOI: https://doi.org/10.1090/S0025-5718-2012-02559-2
Keywords: Robin inverse problem, Tikhonov regularization, finite element method, convergence analysis.
Received by editor(s): September 18, 2010
Received by editor(s) in revised form: February 16, 2011
Published electronically: January 11, 2012
Article copyright: © Copyright 2012 American Mathematical Society