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 -

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.