A priori error analysis for optimal distributed control problem governed by the first order linear hyperbolic equation: Hp-streamline diffusion discontinuous galerkin method

In the current paper, we derive the a priori error analysis (hp version) of the streamline diffusion DG finite element approximation for optimal distributed control problem governed by the first order linear hyperbolic equation. We present the stability of such method, obtain the a priori error upper bound for the state and the control approximation, and prove the convergence of numerical method. For the optimal control problem, these estimates are apparently not available in the literature.