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Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 2/2017

19.10.2016

Indirect Boundary Integral Equation Method for the Cauchy Problem of the Laplace Equation

verfasst von: Yao Sun

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2017

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Abstract

In this paper, we examine the Cauchy problem of the Laplace equation. Motivated by the incompleteness of the single-layer potential function method, we investigate the double-layer potential function method. Through the use of a layer approach to the solution, we devise a numerical method for approximating the solution of the Cauchy problem, which are well known to be highly ill-posed in nature. The ill-posedness is dealt with Tikhonov regularization, whilst the optimal regularization parameter is chosen by Morozov discrepancy principle. Convergence and stability estimates of the proposed method are then given. Finally, some examples are given for the efficiency of the proposed method. Especially, when the single-layer potential function method does not give accurate results for some problems, it is shown that the proposed method is effective and stable.
Nächster Artikel Vertex-Centered Linearity-Preserving Schemes for Nonlinear Parabolic Problems on Polygonal Grids

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Metadaten
Titel
Indirect Boundary Integral Equation Method for the Cauchy Problem of the Laplace Equation
verfasst von
Yao Sun
Publikationsdatum
19.10.2016
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 2/2017
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-016-0308-4

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