Efficient Reconstruction Methods for Nonlinear Elliptic Cauchy Problems with Piecewise Constant Solutions
Year: 2009
Author: Herbert Egger, Antonio Leitao
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 6 : pp. 729–749
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.09-m09S03
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 6 : pp. 729–749
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Nonlinear Cauchy problems Elliptic operators Level-set methods.
Author Details
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