A posteriori error estimators for optimal distributed control governed by the first-order linear hyperbolic equation: DG method

In this article, We analyze the h-version of the discontinuous Galerkin finite element method (DGFEM) for the distributed first-order linear hyperbolic optimal control problems. We derive a posteriori error estimators on general finite element meshes which are sharp in the mesh-width h. These error estimators are shown to be useful in adaptive finite element approximation for the optimal control problems. For the DGFEM we admit very general irregular meshes.