In this paper, we present a posteriori error analysis for hp finite element approximation of convex optimal control problems. We derive a new quasi-interpolation operator of Clment type and a new quasi-interpolation operator of ScottZhang type that preserves homogeneous boundary condition. The ScottZhang type quasi-interpolation is suitable for an application in bounding the errors in L2-norm. Then hp 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. © 2011 Elsevier B.V. All rights reserved.
Chen, Y., & Lin, Y. (2011). A posteriori error estimates for hp finite element solutions of convex optimal control problems. Journal of Computational and Applied Mathematics, 235(12), 3435–3454. https://doi.org/10.1016/j.cam.2011.02.004