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

Published online by Cambridge University Press:  28 May 2015

T. Wei ,
H. H. Qin  and
H. W. Zhang
T. Wei*
Affiliation:
School of Mathematics and Statistics, Lanzhou University, P. R. China
H. H. Qin
Affiliation:
School of Mathematics and Statistics, Lanzhou University, P. R. China
H. W. Zhang
Affiliation:
School of Mathematics and Statistics, Lanzhou University, P. R. China
*
Corresponding author.Email address:tingwei@lzu.edu.cn
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Abstract

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.

Keywords

65N1265N1565N2065N21Cauchy problemLaplace equationregularization methodsconvergence estimates
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 4 , November 2011 , pp. 459 - 477
Copyright
Copyright © Global Science Press Limited 2011

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