A regularization method for a Cauchy problem of Laplace's equation in an annular domain |
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Authors: | T Wei YG Chen |
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Affiliation: | 1. School of Mathematics and Statistics, Lanzhou University, Gansu 730000, PR China;2. School of Mathematics and Computational Science, China University of Petroleum (East China), Shandong 257061, PR China |
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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. |
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Keywords: | Convergence analysis Method of fundamental solutions Cauchy problem for Laplace equation |
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