An abstract framework for elliptic inverse problems: Part 1. An output least-squares approach
Document Type
Article
Publication Date
6-1-2007
Abstract
The solution of an elliptic boundary value problem is an infinitely differentiable function of the coefficient in the partial differential equation. When the (coefficient-dependent) energy norm is used, the result is a smooth, convex output least-squares functional. Using total variation regularization, it is possible to estimate discontinuous coefficients from interior measurements. The minimization problem is guaranteed to have a solution, which can be obtained in the limit from finite-dimensional discretizations of the problem. These properties hold in an abstract framework that encompasses several interesting problems: the standard (scalar) elliptic BVP in divergence form, the system of isotropic elasticity, and others.
Publication Title
Mathematics and Mechanics of Solids
Recommended Citation
Gockenbach, M.,
&
Khan, A. A.
(2007).
An abstract framework for elliptic inverse problems: Part 1. An output least-squares approach.
Mathematics and Mechanics of Solids,
12(3), 259-276.
http://doi.org/10.1177/1081286505055758
Retrieved from: https://digitalcommons.mtu.edu/math-fp/12
Publisher's Statement
Copyright 2007 SAGE Publications. Publisher's version of record: https://doi.org/10.1177/1081286505055758