A numerical method for parameter identification of a boundary value problem

Abstract

A finite element method based on a least-squares mixed formulation is presented to estimate the coefficient in a boundary value problem. Error estimates are obtained in weighted norms of various function spaces which lead to useful rules for choosing regularization parameters and finite element spaces. The cost functional has a structure suitable for efficient finite element implementation. Common minimization algorithms are shown to converge. A multi-level Newton iteration procedure is suggested to find the minimizer. Features of the method are also demonstrated by numerical examples.

Keywords:

• Inverse problem
• parameter identification
• finite element
• error estimates
• regularization
• multigrid

^*The work of T. Lin was partially supported by the National Science Foundation under grant DMS-9704621 and the Air Force Office of Scientific Research under grant number F49620-93-1-0280

^*The work of T. Lin was partially supported by the National Science Foundation under grant DMS-9704621 and the Air Force Office of Scientific Research under grant number F49620-93-1-0280

Notes

^*The work of T. Lin was partially supported by the National Science Foundation under grant DMS-9704621 and the Air Force Office of Scientific Research under grant number F49620-93-1-0280