Adaptive finite element approximation of optimal control problems with the integral fractional Laplacian.

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]