Optimal control problem of the two-dimensional modified anomalous subdiffusion equation with discontinuous Galerkin approximation

In this paper, we consider an optimal control problem (OCP) governed by a modified anomalous subdiffusion equation with box constraints on the control. We apply space–time discontinuous Galerkin method to discretize the problem. Specifically, symmetric interior penalty Galerkin method and piecewise discontinuous constant temporal approximations are used. Then, we discuss the equivalence of optimize then discretize and discretize then optimize approaches in a general setting. We derive stability and convergence analysis for the fully discrete problem. At the end, we present some numerical results to measure the numerical rate of convergence.