This work focuses on the inverse problem of identifying a variable parameter in a 2-D scalar elliptic boundary value problem. It is well-known that this inverse problem is highly ill-posed and regularization is necessary for its stable solution. The inverse problem is studied in an optimization framework, which is the most suitable framework for incorporating regularization. This optimization problem is a constrained optimization problem where the constraint set is a closed and convex set of the admissible coefficients. As an objective functional, we use both the output least squares and modified output least squares functionals. It is known that the most commonly used iterative schemes for such problems require strong monotonicity of the objective functionals derivative. In the context of the considered inverse problem, this is a very stringent requirement and is achieved through a careful selection of the regularization parameter. In contrast, extragradient type methods only require the derivative of the objective functional to be monotone and this allows a greater flexibility for the selection of the regularization parameter. In this work, we use the finite element method for the discretization of the inverse problem and apply the most commonly studied extragradient methods.

Library of Congress Subject Headings

Boundary value problems--Numerical solutions; Differential equations, Elliptic--Numerical solutions; Inverse problems (Differential equations)

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School of Mathematical Sciences (COS)


Khan, Akhtar


Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works. Physical copy available through RIT's The Wallace Library at: QA379 .S37 2013


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