Finite Element Approximation of Optimal Control for the Heat Equation with End-Point State Constraints
Year: 2012
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 4 : pp. 844–875
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-IJNAM-662
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 4 : pp. 844–875
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Error estimate optimal control problem the heat equation end-point state constraint discrete.