Numerical analysis of an energy-like minimization method to solve the Cauchy problem with noisy data

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article

Rischette, R.¹  Baranger, T. N.¹  Debit, N.² 

[1] Univ Lyon 1, CNRS, LaMCoS UMR5259, INSA Lyon, F-69621 Villeurbanne, France

[2] Univ Lyon 1, CNRS, Inst Camille Jordan, F-69622 Villeurbanne, France

关键词: Inverse problem;    Noisy Cauchy problem;    Data completion;    Boundary condition identification;    Finite element method;    A priori error estimates;   

DOI  :  10.1016/j.cam.2010.12.019

来源: Elsevier

【 摘 要 】

This paper is concerned with solving the Cauchy problem for an elliptic equation by minimizing an energy-like error functional and by taking into account noisy Cauchy data. After giving some fundamental results, numerical convergence analysis of the energy-like minimization method is carried out and leads to adapted stopping criteria for the minimization process depending on the noise rate. Numerical examples involving smooth and singular data are presented. (C) 2010 Elsevier BM. All rights reserved.

【 授权许可】

Free