Variational method for multiple parameter identification in elliptic PDEs

In the present paper we investigate the inverse problem of identifying simultaneously the diffusion matrix, source term and boundary condition in the Neumann boundary value problem for an elliptic partial differential equation (PDE) from a measurement data, which is weaker than required of the exact...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2018-05, Vol.461 (1), p.676-700
Main Author: Quyen, Tran Nhan Tam
Format: Article
Language:English
Subjects:
Boundary condition
Diffusion matrix
Finite element method
Ill-posed problem
Multiple parameter identification
Source term
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Summary:In the present paper we investigate the inverse problem of identifying simultaneously the diffusion matrix, source term and boundary condition in the Neumann boundary value problem for an elliptic partial differential equation (PDE) from a measurement data, which is weaker than required of the exact state. A variational method based on energy functions with Tikhonov regularization is here proposed to treat the identification problem. We discretize the PDE with the finite element method and prove the convergence as well as analyze error bounds of this approach.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2018.01.030