Abstract
In this paper we study the variational discretization and mixed finite element methods for optimal control problem governed by semilinear parabolic equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. We derive a priori error estimates for the coupled state and the control approximation of the semilinear parabolic optimal control problems. Finally, we present a numerical example which confirms our theoretical results.
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