Title

Numerical analysis of elliptic inverse problems with interior data

Authors

Mark Gockenbach, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

2008

Abstract

A number of algorithms have been proposed and analyzed for estimating a coefficient in an elliptic boundary value problem when interior data is available. Most of the analysis has been done for the simple scalar BVP

-Δ a Δ u = f in Ω,

a (∂ u / ∂ n) g on ∂ Ω

However, some methods and the associated analysis have been extended to the problem of estimating the Lamé moduli in the system of linear, isotropic elasticity. Under certain idealized conditions, convergence of estimates to the exact Lame moduli has been proved for two techniques, the output least-squares method and a variational method similar to the equation error approach.

Publisher's Statement

© 2008 IOP Publishing Ltd. Publisher's version of record: https://doi.org/10.1088/1742-6596/124/1/012026

Publication Title

Journal of Physics: Conference Series

Recommended Citation

Gockenbach, M. (2008). Numerical analysis of elliptic inverse problems with interior data. Journal of Physics: Conference Series, 124(1). http://doi.org/10.1088/1742-6596/124/1/012026
Retrieved from: https://digitalcommons.mtu.edu/math-fp/21

Version

Publisher's PDF