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In this paper, we study an adaptive finite element approximation of optimal control problems with integral fractional Laplacian and pointwise control constraints. The state variable is approximated by piecewise linear polynomials, and the control variable is implicitly discretized. Upper and lower bounds of a posteriori error estimates for finite element approximation of the optimal control problem are derived. An h-adaptive algorithm driven by the a posterior error estimator is presented with Dörfler’s marking criterion. We prove that the adaptive algorithm yields a sequence of approximations that converge at the optimal algebraic rate. Numerical examples are given to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper a posteriori error estimate for continuous interior penalty Galerkin approximation of transient convection dominated diffusion optimal control problems with control constraints is presented. The state equation is discretized by the continuous interior penalty Galerkin method with continuous piecewise linear polynomial space and the control variable is approximated by implicit discretization concept. By use of the elliptic reconstruction technique proposed for parabolic equations, a posteriori error estimates for state variable, adjoint state variable and control variable are proved, which can be used to guide the mesh refinement in the adaptive algorithm. [ABSTRACT FROM AUTHOR]