A C0 interior penalty method for the Dirichlet control problem governed by biharmonic operator

An energy space based Dirichlet boundary control problem governed by biharmonic equation is investigated and subsequently a C0-interior penalty method is proposed and analyzed. An abstract a priori error estimate is derived under the minimal regularity conditions. The abstract error estimate guarantees optimal order of convergence whenever the solution is sufficiently regular. Further an optimal order L2-norm error estimate is derived. Numerical experiments illustrate the theoretical findings.