Richardson Extrapolation and Defect Correction of Finite Element Methods for Optimal Control Problems (Journal of Computational Mathematics, 2018)
Asymptotic error expansions in $H^1$-norm for the bilinear finite element approximation to a class of optimal control problems are derived for rectangular meshes. With the rectangular meshes, the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied. The higher order numerical approximations are used to generate a posteriori error estimators for the finite element approximation.