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A regularization method for a Cauchy problem of Laplace's equation in an annular domain

Author

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  • Wei, T.
  • Chen, Y.G.

Abstract

In this paper, we propose a new regularization method based on a finite-dimensional subspace generated from fundamental solutions for solving a Cauchy problem of Laplace's equation in an annular domain. Based on a conditional stability for the Cauchy problem of Laplace's equation, we obtain a convergence estimate under the suitable choice of a regularization parameter and an a-priori bound assumption on the solution. A numerical example is provided to show the effectiveness of the proposed method from both accuracy and stability.

Suggested Citation

  • Wei, T. & Chen, Y.G., 2012. "A regularization method for a Cauchy problem of Laplace's equation in an annular domain," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(11), pages 2129-2144.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:11:p:2129-2144
    DOI: 10.1016/j.matcom.2012.05.009
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