Title

Stability and error estimates for an equation error method for elliptic equations

Authors

Mohammad F. Al-Jamal, Michigan Technological University
Mark Gockenbach, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

8-7-2012

Abstract

To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be implemented in a practical algorithm. Numerical experiments demonstrate the efficacy and limitations of the method.

Publisher's Statement

Publisher's version of record: https://doi.org/10.1088/0266-5611/28/9/095006

Publication Title

Inverse Problems

Recommended Citation

Al-Jamal, M. F., & Gockenbach, M. (2012). Stability and error estimates for an equation error method for elliptic equations. Inverse Problems, 28(9). http://doi.org/10.1088/0266-5611/28/9/095006
Retrieved from: https://digitalcommons.mtu.edu/math-fp/20