JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (2): 18-24.doi: 10.6040/j.issn.1671-9352.0.2017.292

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A posteriori choice rule for the mollification regularization parameter for the Cauchy problem of an elliptic equation

DING Feng-xia, CHENG Hao*   

  1. School of Science, Jiangnan University, Wuxi 214122, Jiangsu, China
  • Received:2017-06-14 Online:2018-02-20 Published:2018-01-31

Abstract: We transform the ill-posed problem into a well-posed problem by convolutioning the Gaussian function with parameters and the measurement data. A posteriori parameter choice rule is given which is based on Morozovs discrepancy principle and the error estimates between the exact solution and its approximation are also given. Numerical experiments show the validity of mollification regularization posteriori parameter choice rule.

Key words: mollification regularization method, posteriori parameter choice, error estimation, the Cauchy problem of an elliptic equation, numerical experiment

CLC Number: 

  • O241.8
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