| There is a broad range of mathematical problems that can be classified under the title of inverse problems. In this thesis we concern ourselves with the inverse problem of identifying variable coefficients from observation data given an underlying fourth-order or parabolic partial differential equation. We focus on the methods that are employed to derive the gradient of the output least-squares, modified output least-squares, and equation error approach cost functionals. We show the complete derivation of equations, computation of finite element matrices necessary to find the solution of the inverse problem, and display numerical results achieved by numerical implementation of finite element method discretization. |
