An interior penalty method for distributed optimal control problems governed by the biharmonic operator
In this paper, a C0 C 0 interior penalty method has been proposed and analyzed for distributed optimal control problems governed by the biharmonic operator. The state and adjoint variables are discretized using continuous piecewise quadratic finite elements while the control variable is discretized using piecewise constant approximations. A priori and a posteriori error estimates are derived for the state, adjoint and control variables under minimal regularity assumptions. Numerical results justify the theoretical results obtained. The a posteriori error estimators are useful in adaptive finite element approximation and the numerical results indicate that the sharp error estimators work efficiently in guiding the mesh refinement.
distributed optimal control problems biharmonic operator a posteriori error estimate c0 c 0 interior penalty method c0 c 0 c0 c 0 c 0 a priori error estimate