Advisory Committee Chair
Ian W Knowles
Advisory Committee Members
Ryoichi Kawai
Tsun Zee Mai
Sivaguru S Ravindran
Yanni Zeng
Document Type
Dissertation
Date of Award
2010
Degree Name by School
Doctor of Philosophy (PhD) College of Arts and Sciences
Abstract
Inverse problems involving elliptic partial differential equations have many physical applications. In 1993, Knowles & Wallace published a variational method of numerical differentiation involving minimization of an energy functional formed from the solution of an associated elliptic equation. This method has been successfully used to estimate the values of the parameters of the groundwater flow equation. The primary focus of this dissertation will be a proof of the stability of this inverse problem. Additionally, I will present theoretical error bounds on the data surface that is constructed for the parameter recovery and results of testing a new numerical algorithm.
Recommended Citation
La Russa, Mary Antoinette, "Conditional Well-Posedness and Error Bounds for the Groundwater Inverse Problem" (2010). All ETDs from UAB. 2224.
https://digitalcommons.library.uab.edu/etd-collection/2224