A Numerical Approximation Method for the Inverse Problem of the Three-Dimensional Laplace Equation

Mathematics

Shangqin He¹  Xiufang Feng¹ 

[1] School of Mathematics and Statistics, NingXia University, Yinchuan 750021, China;

关键词: three-dimensional Laplace equation;    ill-posed;    de la Vallée Poussin kernel;    mollification method;    regular parameter;    error estimate;   

DOI  :  10.3390/math7060487

来源: DOAJ

【 摘 要 】

In this article, an inverse problem with regards to the Laplace equation with non-homogeneous Neumann boundary conditions in a three-dimensional case is investigated. To deal with this problem, a regularization method (mollification method) with the bivariate de la Vallée Poussin kernel is proposed. Stable estimates are obtained under a priori bound assumptions and an appropriate choice of the regularization parameter. The error estimates indicate that the solution of the approximation continuously depends on the noisy data. Two experiments are presented, in order to validate the proposed method in terms of accuracy, convergence, stability, and efficiency.

【 授权许可】

Unknown