@Article{AAMM-1-6,
author = {Herbert, Egger and Leitao, Antonio},
title = {Efficient Reconstruction Methods for Nonlinear Elliptic Cauchy Problems with Piecewise Constant Solutions},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2009},
volume = {1},
number = {6},
pages = {729--749},
abstract = {<p style="text-align: justify;">In this article, a level-set approach for solving nonlinear elliptic Cauchy problems with piecewise constant solutions is proposed, which 
allows the definition of a Tikhonov functional on a space of 
level-set functions. We provide convergence analysis for the 
Tikhonov approach, including stability and convergence results. Moreover, a numerical investigation of the proposed Tikhonov regularization
method is presented. 
Newton-type methods are used for the solution of the optimality systems, 
which can be interpreted as stabilized versions of algorithms in a previous
work and yield a substantial improvement in performance. The whole approach is focused on three dimensional models, better suited 
for real life applications.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.09-m09S03},
url = {https://global-sci.com/article/73711/efficient-reconstruction-methods-for-nonlinear-elliptic-cauchy-problems-with-piecewise-constant-solutions}
}