Stability analysis of the harmonic polynomial method for the Cauchy problem of Laplace's equation

被引：2

作者：

Zhang, Deyue ^{[1
]}

Sun, Wei ^{[2
]}

机构：

[1] Jilin Univ, Coll Math, Changchun 130023, Peoples R China

[2] Harbin Univ Sci & Technol, Sch Appl Sci, Harbin, Peoples R China

来源：

APPLICABLE ANALYSIS | 2014年 / 93卷 / 10期

关键词：

Cauchy problems; Carleman estimate; harmonic polynomial; stability;

D O I：

10.1080/00036811.2013.867020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the Cauchy problem connected with the Laplace equation in a smooth bounded domain. The harmonic polynomial method with Tikhonov regularization is applied to achieve a regularized solution to the problem with noisy data. The convergence and stability are obtained with a suitable choice of the regularization parameter. Numerical experiments are also presented to show the effectiveness of the proposed method.

引用

页码：2076 / 2092

页数：17

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