Volume 1, Issue 6
Efficient Reconstruction Methods for Nonlinear Elliptic Cauchy Problems with Piecewise Constant Solutions

Herbert Egger and Antonio Leitao

10.4208/aamm.09-m09S03

Adv. Appl. Math. Mech., 1 (2009), pp. 729-749.

Preview Full PDF BiBTex 100 359
  • 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.

  • History

Published online: 2009-01

  • AMS Subject Headings

65J20, 35J60

  • Cited by