## Numerical identification of a Robin coefficient in parabolic problems

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**81**(2012), 1369-1398 Request permission

## 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.## References

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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
- MR Author ID: 741824
- 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
- Received by editor(s): September 18, 2010
- Received by editor(s) in revised form: February 16, 2011
- Published electronically: January 11, 2012
- © Copyright 2012 American Mathematical Society
- Journal: Math. Comp.
**81**(2012), 1369-1398 - MSC (2010): Primary 65M30, 65M32, 65M12
- DOI: https://doi.org/10.1090/S0025-5718-2012-02559-2
- MathSciNet review: 2904583