A posteriori error estimates for hp finite element solutions of convex optimal control problems

In this paper, we present a posteriori error analysis for hphp finite element approximation of convex optimal control problems. We derive a new quasi-interpolation operator of Clément type and a new quasi-interpolation operator of Scott–Zhang type that preserves homogeneous boundary condition. The Scott–Zhang type quasi-interpolation is suitable for an application in bounding the errors in L2L2-norm. Then hphp a posteriori error estimators are obtained for the coupled state and control approximations. Such estimators can be used to construct reliable adaptive finite elements for the control problems.