A Ciarlet-Raviart Mixed Finite Element Method for Optimal Control Problems Governed by a Fourth Order Bi-Wave Equation

Abstract

The optimal control problem governed by a stationary fourth-order bi-wave equation is considered. To tackle this problem, we propose a bilinear mixed method of the Ciarlet-Raviart type. Our method exhibits an optimal convergence rate in the $L^2$-norm and demonstrates a global supercloseness property in the $H^1$ -seminorm. Moreover, through the application of an interpolation post-processing technique, the method achieves global superconvergence. We provide two numerical examples to numerically validate these theoretical properties of our proposed method.