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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:271

Article

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

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

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

关键词: Inverse problem;    Cauchy problem;    Data completion;    Boundary condition identification;    Noise;    A priori error estimates;   

DOI  :  10.1016/j.cam.2014.03.024

来源: Elsevier

【 摘 要 】

This paper is concerned with solving the Cauchy problem for the parabolic 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 an adapted stopping criteria depending on noise rate for the minimization process. Numerical experiments are performed and confirm the theoretical convergence order and the good behavior of the minimization process. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free