@Article{CiCP-9-878,
author = {Houde Han, Leevan Ling and Tomoya Takeuchi},
title = {An Energy Regularization for Cauchy Problems of Laplace Equation in Annulus Domain},
journal = {Communications in Computational Physics},
year = {2011},
volume = {9},
number = {4},
pages = {878--896},
abstract = {<p style="text-align: justify;">Detecting corrosion by electrical field can be modeled by a Cauchy problem
of Laplace equation in annulus domain under the assumption that the thickness of the
pipe is relatively small compared with the radius of the pipe. The interior surface of the
pipe is inaccessible and the nondestructive detection is solely based on measurements
from the outer layer. The Cauchy problem for an elliptic equation is a typical ill-posed
problem whose solution does not depend continuously on the boundary data. In this
work, we assume that the measurements are available on the whole outer boundary on
an annulus domain. By imposing reasonable assumptions, the theoretical goal here is
to derive the stabilities of the Cauchy solutions and an energy regularization method.
Relationship between the proposed energy regularization method and the Tikhonov
regularization with Morozov principle is also given. A novel numerical algorithm is
proposed and numerical examples are given.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.200110.060910a},
url = {http://global-sci.org/intro/article_detail/cicp/7526.html}
}