Date of Completion
8-19-2016
Embargo Period
10-24-2016
Keywords
Finite Element Methods, Optimal Control Problems, Dirichlet Boundary Conditions, DG methods, Numerical Analysis.
Major Advisor
Dmitriy Leykekhman
Associate Advisor
Yung-Sze Choi
Associate Advisor
Joseph McKenna
Field of Study
Mathematics
Degree
Doctor of Philosophy
Open Access
Open Access
Abstract
In the present work, we consider Symmetric Interior Penalty Galerkin (SIPG) method to approximate the solution to Dirichlet optimal control problem governed by a linear advection-diffusion-reaction equation on a convex polygonal domain.
The main feature of the method is that Dirichlet boundary conditions enter naturally into bilinear form and the finite element analysis can be performed in the standard setting. Another advantage of the method is that the method is stable and can be of arbitrary high degree. We show existence and uniqueness of the analytical and discrete solutions of the problem and derive optimal error estimates for the control on general convex polygonal domains.
Finally, we support our main results and highlight some of the features of the method with the several numerical examples in one and two dimensions. We also investigate numerically the performance of the method for advection-dominated problems.
Recommended Citation
Corekli, Cagnur, "Finite Element Methods of Dirichlet Boundary Optimal Control Problems With Weakly Imposed Boundary Conditions" (2016). Doctoral Dissertations. 1245.
https://digitalcommons.lib.uconn.edu/dissertations/1245