Date of Award
Doctor of Philosophy in Mathematical Sciences (PhD)
College, School or Department Name
Department of Mathematical Sciences
Mark S Gockenbach
To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be implemented in a practical algorithm. Numerical experiments demonstrate the efficacy and limitations of the method.
Al-Jamal, Mohammad F., "Numerical solutions of elliptic inverse problems via the equation error method", Dissertation, Michigan Technological University, 2012.