@Article{IJNAM-9-844,
author = {G. Wang and L. Wang},
title = {Finite Element Approximation of Optimal Control for the Heat Equation with End-Point State Constraints},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2012},
volume = {9},
number = {4},
pages = {844--875},
abstract = {<p style="text-align: justify;">This study presents a new finite element approximation for an optimal control problem
($P$) governed by the heat equation and with end-point state constraints. The state constraint set $S$ is assumed to have an empty interior in the state space. We begin with building a new penalty
functional where the penalty parameter is an algebraic combination of the mesh size and the time
step. Based on it, we establish a discrete optimal control problem ($P_{h\tau}$) without state constraints.
With the help of Pontryagin’s maximum principle and by suitably choosing the above-mentioned
combination, we successfully derive error estimate between optimal controls of problems ($P$) and
($P_{h\tau}$), in terms of the mesh size and time step.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/662.html}
}