Finite element analysis for identifying the reaction coefficient in PDE from boundary observations

This work is devoted to the nonlinear inverse problem of identifying the reaction coefficient in an elliptic boundary value problem from single Cauchy data on a part of the boundary. We then examine simultaneously two elliptic boundary value problems generated from the available Cauchy data. The out...

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Bibliographic Details
Published in:Applied numerical mathematics 2019-11, Vol.145, p.297-314
Main Author: Quyen, Tran Nhan Tam
Format: Article
Language:English
Subjects:
Boundary observation
Finite element method
Ill-posed problem
Mixed problem
Neumann problem
Reaction coefficient identification
Tikhonov regularization
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Summary:This work is devoted to the nonlinear inverse problem of identifying the reaction coefficient in an elliptic boundary value problem from single Cauchy data on a part of the boundary. We then examine simultaneously two elliptic boundary value problems generated from the available Cauchy data. The output least squares method with the Tikhonov regularization is applied to find approximations of the sought coefficient. We discretize the PDEs with piecewise linear finite elements. The stability and convergence of this technique are then established. A numerical experiment is presented to illustrate our theoretical findings.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2019.06.015