@Article{AAMM-16-1152,
author = {Tao , Xuelin},
title = {Error Estimates for Finite Element Approximation to Elliptic Optimal Control Problems with Boundary Observations in $H^{-\frac{1}{2}}(\Gamma)$},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2024},
volume = {16},
number = {5},
pages = {1152--1175},
abstract = {<p style="text-align: justify;">In this paper we consider the finite element approximation to an elliptic
optimal control problem with boundary observations in $H^{-\frac{1}{2}}(\Gamma).$ This problem is motivated by certain applications in optimal control of semiconductor devices where the
discrepancy of the current density on the boundary to the target one is the objective to
be minimized. The observation in $H^{-\frac{1}{2}}(\Gamma)$ is realized through a Neumann-to-Dirichlet
mapping which facilitates the theoretical and numerical analysis. A priori error estimate for the optimal control is derived based on the variational control discretization,
whereas the state and adjoint state variables are approximated by piecewise linear and
continuous finite elements. Second order convergence rate for the optimal control is
theoretically proved and verified by numerical results.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2022-0172},
url = {http://global-sci.org/intro/article_detail/aamm/23289.html}
}