Volume 4, Issue 4
Convergence Estimates for Some Regularization Methods to Solve a Cauchy Problem of the Laplace Equation

T. Wei, H. H. Qin & H. W. Zhang

Numer. Math. Theor. Meth. Appl., 4 (2011), pp. 459-477.

Published online: 2011-04

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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

Cauchy problem, Laplace equation, regularization methods, convergence estimates.

  • AMS Subject Headings

65N12, 65N15, 65N20, 65N21

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-4-459, author = {}, title = {Convergence Estimates for Some Regularization Methods to Solve a Cauchy Problem of the Laplace Equation}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2011}, volume = {4}, number = {4}, pages = {459--477}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2011.m1015}, url = {http://global-sci.org/intro/article_detail/nmtma/5978.html} }
TY - JOUR T1 - Convergence Estimates for Some Regularization Methods to Solve a Cauchy Problem of the Laplace Equation JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 459 EP - 477 PY - 2011 DA - 2011/04 SN - 4 DO - http://doi.org/10.4208/nmtma.2011.m1015 UR - https://global-sci.org/intro/article_detail/nmtma/5978.html KW - Cauchy problem, Laplace equation, regularization methods, convergence estimates. AB -

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.

T. Wei, H. H. Qin & H. W. Zhang. (2020). Convergence Estimates for Some Regularization Methods to Solve a Cauchy Problem of the Laplace Equation. Numerical Mathematics: Theory, Methods and Applications. 4 (4). 459-477. doi:10.4208/nmtma.2011.m1015
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