Modified C0 interior penalty analysis for fourth order Dirichlet boundary control problem and a posteriori error estimate

We revisit the L2 norm error estimate for the C0 interior penalty analysis of fourth order Dirichlet boundary control problem. The L2 norm estimate for the optimal control is derived under reduced regularity assumption and this analysis can be carried out on any convex polygonal domains. Residual based a-posteriori error bounds are derived for optimal control, state and adjoint state variables under minimal regularity assumptions. The estimators are shown to be reliable and locally efficient. The theoretical findings are illustrated by numerical experiments.