Dissertation/Thesis Abstract

Conditional well-posedness and error bounds for the groundwater inverse problem
by LaRussa, Mary Antoinette, Ph.D., The University of Alabama at Birmingham, 2010, 443; 3438574
Abstract (Summary)

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.

Keywords: Inverse problems, conditional well-posedness, parameter estimation, error bounds, groundwater

Indexing (document details)
Advisor: Knowles, Ian W.
Commitee: Kawai, Ryoichi, Mai, Tsun Zee, Ravindran, Sivaguru S., Zeng, Yanni
School: The University of Alabama at Birmingham
Department: Applied Mathematics
School Location: United States -- Alabama
Source: DAI-B 72/03, Dissertation Abstracts International
Subjects: Applied Mathematics, Hydrologic sciences
Keywords: Conditional well-posedness, Error bounds, Groundwater, Inverse problems, Parameter estimation
Publication Number: 3438574
ISBN: 978-1-124-42780-5
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