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

作者：Wei, T.^*; Chen, Y. G.

来源：Mathematics and Computers in Simulation, 2012, 82(11): 2129-2144.

DOI：10.1016/j.matcom.2012.05.009

• Convergence analysis
• Method of fundamental solutions
• Cauchy problem for Laplace equation

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.

• 出版日期2012-7
• 单位兰州大学