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

Abstract

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.

Keywords:

• Cauchy problems
• Carleman estimate
• harmonic polynomial
• stability

AMS Subject Classifications:

• 35N25
• 35R25
• 65N12

Acknowledgments

The research was supported by the NSFC (11271159) and Education Department of Heilongjiang (12531136).