Date of Award
Doctor of Philosophy
M. D. Gunzburger
L. S. Hou
We present some results concerning boundary optimal control problems and related initial-boundary value problems. We prove the existence and uniqueness of the solution of a parabolic saddle point problem, as well as the existence and uniqueness of a penalized and an iterated penalized saddle point problem. Moreover, we derive semidiscrete error estimates for the finite element approximation of the penalized saddle point problem, and semidiscrete error estimates for the penalized and unpenalized heat equation with nonhomogeneous boundary data under minimal regularity assumptions. Finally, we use the above results for the analysis and finite element analysis of boundary optimal control problems having states constrained to parabolic partial differential equations.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu
Chrysafinos, Konstantinos, "Analysis and finite element approximations of parabolic saddle point problems with applications to optimal control " (2002). Retrospective Theses and Dissertations. 365.