Variational discretization for optimal control problems governed by parabolic equations

• DOI: 10.1007/s11424-013-1166-x
• Publication Date: 2013-03-31T23:45:03Z
• Authors: Yanping Chen; Tianliang Hou; Nianyu Yi
• Keywords: 0101 mathematics; 01 natural sciences

This paper considers the variational discretization for the constrained optimal control problem governed by linear parabolic equations. The state and co-state are approximated by Raviart-Thomas mixed finite element spaces, and the authors do not discretize the space of admissible control but implicitly utilize the relation between co-state and control for the discretization of the control. A priori error estimates are derived for the state, the co-state, and the control. Some numerical examples are presented to confirm the theoretical investigations.