Gradient schemes for optimal control problems, with super-convergence for non-conforming finite elements and mixed-hybrid mimetic finite differences

Jerome Droniou, Neela Nataraj, S. Devika

Published 2016-08-05Version 1

In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of gradient schemes. A gradient scheme is defined for the optimality system of the control problem. Error estimates for state, adjoint and control variables are derived. Superconvergence results for gradient schemes under realistic regularity assumptions on the exact solution is discussed. Results of numerical experiments are demonstrated for the conforming, nonconforming and mixed-hybrid mimetic finite difference schemes.