An inverse Robin problem for Laplace's equation: theoretical results and numerical methods
- 1 January 1999
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 15 (1) , 41-48
- https://doi.org/10.1088/0266-5611/15/1/008
Abstract
We consider the problem of detecting corrosion damage on an inaccessible part of a metallic specimen. Electrostatic data are collected on an accessible part of the boundary. The adoption of a simplified model of corrosion appearance reduces our problem to recovering a functional coefficient in a Robin boundary condition for Laplace's equation. We review theoretical results and numerical methods based on the thin-plate approximation and the Galerkin method. Moreover, we introduce a numerical algorithm based on the quasi-reversibility method.Keywords
This publication has 5 references indexed in Scilit:
- An inverse problem in corrosion detectionInverse Problems, 1997
- An Inverse Problem in Thermal ImagingSIAM Journal on Applied Mathematics, 1996
- Method for imaging corrosion damage in thin plates from electrostatic dataInverse Problems, 1996
- Boundary control of heat conductionComputational Mathematics and Modeling, 1996
- A Computational Quasi-Reversibility Method for Cauchy Problems for Laplace’s EquationSIAM Journal on Applied Mathematics, 1991