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

T. Wei and Y.G. Chen

Mathematics and Computers in Simulation (MATCOM), 2012, vol. 82, issue 11, 2129-2144

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.

Keywords: Convergence analysis; Method of fundamental solutions; Cauchy problem for Laplace equation (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:82:y:2012:i:11:p:2129-2144

DOI: 10.1016/j.matcom.2012.05.009

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