Variational method for multiple parameter identification in elliptic PDEs

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:461

Article

Tran Nhan Tam Quyen^1,2 

[1] Univ Hamburg, Dept Math, Bundesstr 55, D-20146 Hamburg, Germany

[2] Univ Gottingen, Inst Numer & Angew Math, Lotzestr 16-18, D-37083 Gottingen, Germany

关键词: Multiple parameter identification;    Diffusion matrix;    Source term;    Boundary condition;    Ill-posed problem;    Finite element method;   

DOI  :  10.1016/j.jmaa.2018.01.030

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free