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

Shangqin He and Xiufang Feng
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Shangqin He: School of Mathematics and Statistics, NingXia University, Yinchuan 750021, China
Xiufang Feng: School of Mathematics and Statistics, NingXia University, Yinchuan 750021, China

Mathematics, 2019, vol. 7, issue 6, 1-13

Abstract: 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.

Keywords: three-dimensional Laplace equation; ill-posed; de la Vallée Poussin kernel; mollification method; regular parameter; error estimate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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