A variational-type method of fundamental solutions for a Cauchy problem of Laplace's equation

作者：Wei, T.^*; Chen, Y. G.; Liu, J. C.

来源：Applied Mathematical Modelling, 2013, 37(3): 1039-1053.

DOI：10.1016/j.apm.2012.03.023

• 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 a simply-connected bounded domain. Based on a global conditional stability for the Cauchy problem of Laplace's equation, the convergence analysis is given under a suitable choice for a regularization parameter and an a-priori bound assumption to the solution. Numerical experiments are provided to support the analysis and to show the effectiveness of the proposed method from both accuracy and stability.

• 出版日期2013-2-1
• 单位兰州大学; 中国石油大学（华东）