TY - JOUR
T1 - Finite Element Approximation of Optimal Control for the Heat Equation with End-Point State Constraints
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 844
EP - 875
PY - 2012
DA - 2012/09
SN - 9
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/662.html
KW - Error estimate, optimal control problem, the heat equation, end-point state constraint, discrete.
AB - <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>