Convergence Estimates for Some Regularization Methods to Solve a Cauchy Problem of the Laplace Equation  

作　　者：T.Wei H.H.Qin H.W.Zhang 

机构地区：[1]School of Mathematics and Statistics,Lanzhou University,P.R.China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2011年第4期459-477,共19页高等学校计算数学学报（英文版）

基　　金：supported by the NSF of China(10971089);the Fundamental Research Funds for the Central Universities(lzujbky-2010-k10).

摘　　要：In this paper,we give a general proof on convergence estimates for some regularization methods to solve a Cauchy problem for the Laplace equation in a rectangular domain.The regularization methods we considered are:a non-local boundary value problem method,a boundary Tikhonov regularization method and a generalized method.Based on the conditional stability estimates,the convergence estimates for various regularization methods are easily obtained under the simple verifications of some conditions.Numerical results for one example show that the proposed numerical methods are effective and stable.

关 键 词：Cauchy problem Laplace equation regularization methods convergence estimates 

分 类 号：O17[理学—数学]