Error analysis of an HDG method for a distributed optimal control problem

In this paper, we present a priori   error analysis of a hybridizable discontinuous Galerkin (HDG) method for a distributed optimal control problem governed by diffusion equations. The error estimates are established based on the projection-based approach recently used to analyze these methods for the diffusion equation. We proved that for approximations of degree kk on conforming meshes, the orders of convergence of the approximation to fluxes and scalar variables are k+1k+1 when the local stabilization parameter is suitably chosen.