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.
|Original language||English (US)|
|Number of pages||30|
|Journal||MATHEMATICS OF COMPUTATION|
|State||Published - 2012|
Bibliographical noteKAUST Repository Item: Exported on 2021-09-17
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: King Abdullah University of Science & Technology
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
ASJC Scopus subject areas
- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics