A MODIFIED TIKHONOV REGULARIZATION METHOD FOR THE CAUCHY PROBLEM OF LAPLACE EQUATION

In this paper, we consider the Cauchy problem for the Laplace equation, which is severely ill-posed in the sense that the solution does not depend continuously on the data. A modified Tikhonov regularization method is proposed to solve this problem. An error estimate for the a priori parameter choic...

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Bibliographic Details
Published in:Acta mathematica scientia 2015-11, Vol.35 (6), p.1339-1348
Main Author: 杨帆 傅初黎 李晓晓
Format: Article
Language:English
Subjects:
35R25
35R30
47A52
a posteriori parameter choice
Cauchy problem for Laplace equation
error estimate
ill-posed problem
参数选择
拉普拉斯方程
拉氏方程
数值算例
柯西问题
正则化方法
误差估计
选择规则
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Summary:In this paper, we consider the Cauchy problem for the Laplace equation, which is severely ill-posed in the sense that the solution does not depend continuously on the data. A modified Tikhonov regularization method is proposed to solve this problem. An error estimate for the a priori parameter choice between the exact solution and its regularized approximation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained. Numerical examples illustrate the validity and effectiveness of this method.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(15)30058-8