Solving Cauchy problems by minimizing an energy-like functional

An energy-like error functional is introduced in the context of the ill-posed problem of boundary data recovering, which is well known as a Cauchy problem. Links with existing methods for data completion are detailed. Here the problem is converted into an optimization problem; the computation of the...

Full description

Saved in:
Bibliographic Details
Published in:Inverse problems 2006-02, Vol.22 (1), p.115-133
Main Authors: Andrieux, S, Baranger, T N, Abda, A Ben
Format: Article
Language:English
Subjects:
Analysis of PDEs
Engineering Sciences
Exact sciences and technology
Mathematics
Mechanics
Numerical Analysis
Optimization and Control
Physics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:An energy-like error functional is introduced in the context of the ill-posed problem of boundary data recovering, which is well known as a Cauchy problem. Links with existing methods for data completion are detailed. Here the problem is converted into an optimization problem; the computation of the gradients of the energy-like functional is given for both the continuous and the discrete problems. Numerical experiments highlight the efficiency of the proposed method as well as its robustness in the model context of Laplace's equation, but also for anisotropic conductivity problems.
ISSN:0266-5611
1361-6420
DOI:10.1088/0266-5611/22/1/007