Adaptive wavelet schemes for an elliptic control problem with Dirichlet boundary control

2005 ◽  
Vol 39 (1-3) ◽  
pp. 199-220 ◽  
Author(s):  
Angela Kunoth
Keyword(s):  
Control Problem ◽  
Boundary Control ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Control ◽  
Adaptive Wavelet

scholarly journals Crank-Nicolson finite difference schemes for parabolic optimal Dirichlet boundary control problem

2021 ◽  
Author(s):  
Caijie Yang ◽  
Tongjun Sun
Keyword(s):  
Finite Difference ◽  
Control Problem ◽  
Boundary Control ◽  
Dirichlet Boundary ◽  
Second Order ◽  
Difference Schemes ◽  
Optimality System ◽  
Finite Difference Schemes ◽  
Dirichlet Boundary Control ◽  
Boundary Control Problem

In this paper, we adopt the optimize-then-discretize approach to solve parabolic optimal Dirichlet boundary control problem. First, we derive the first-order necessary optimality system, which includes the state, co-state equations and the optimality condition. Then, we propose Crank-Nicolson finite difference schemes to discretize the optimality system in 1D and 2D cases, respectively. In order to build the second order spatial approximation, we use the ghost points on the boundary in the schemes. We prove that the proposed schemes are unconditionally stable, compatible and second-order convergent in both time and space. To avoid solving the large coupled schemes directly, we use the iterative method. Finally, we present a numerical example to validate our theoretical analysis.

scholarly journals Error bounds for a Dirichlet boundary control problem based on energy spaces

2016 ◽  
Vol 86 (305) ◽  
pp. 1103-1126 ◽  
Author(s):  
Sudipto Chowdhury ◽  
Thirupathi Gudi ◽  
A. K. Nandakumaran
Keyword(s):  
Control Problem ◽  
Boundary Control ◽  
Error Bounds ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Control ◽  
Boundary Control Problem

Finite element analysis of the constrained Dirichlet boundary control problem governed by the diffusion problem

2020 ◽  
Vol 26 ◽  
pp. 78
Author(s):  
Thirupathi Gudi ◽  
Ramesh Ch. Sau
Keyword(s):  
Finite Element ◽  
Control Problem ◽  
Dirichlet Boundary ◽  
A Priori ◽  
Diffusion Problem ◽  
Discrete Control ◽  
Optimal Order ◽  
Control Constraints ◽  
Element Analysis ◽  
Dirichlet Boundary Control

We study an energy space-based approach for the Dirichlet boundary optimal control problem governed by the Laplace equation with control constraints. The optimality system results in a simplified Signorini type problem for control which is coupled with boundary value problems for state and costate variables. We propose a finite element based numerical method using the linear Lagrange finite element spaces with discrete control constraints at the Lagrange nodes. The analysis is presented in a combination for both the gradient and the L2 cost functional. A priori error estimates of optimal order in the energy norm is derived up to the regularity of the solution for both the cases. Theoretical results are illustrated by some numerical experiments.

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