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

Author

Listed:
  • Shangqin He

    (School of Mathematics and Statistics, NingXia University, Yinchuan 750021, China
    College of Mathematics and Information Science and Technology, Hebei Normal University of Science and Technology, Qinhuangdao 066004, China)

  • Xiufang Feng

    (School of Mathematics and Statistics, NingXia University, Yinchuan 750021, China)

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.

Suggested Citation

  • Shangqin He & Xiufang Feng, 2019. "A Numerical Approximation Method for the Inverse Problem of the Three-Dimensional Laplace Equation," Mathematics, MDPI, vol. 7(6), pages 1-13, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:487-:d:234991
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