A mixed finite element method using a biorthogonal system for optimal control problems governed by a biharmonic equation

作者：Bishnu P. Lamichhane, N. Nataraj, Deepanshu Verma · 发表于：ANZIAM Journal · 年份：2023 · DOI：10.21914/anziamj.v64.17961

In this article, we consider an optimal control problem governed by a biharmonic equation with clamped boundary conditions. We use the Ciarlet--Raviart formulation combined with a biorthogonal system to obtain an efficient numerical scheme. We discuss the a priori error analysis and present results of the numerical experiments that validate the theoretical estimates. References L. Boudjaj, A. Naji, and F. Ghafrani. Solving biharmonic equation as an optimal control problem using localized radial basis functions collocation method. Eng. Anal. Bound. Elements 107 (2019), pp. 208–217. doi: 10.1016/j.enganabound.2019.07.007 W. Cao and D. Yang. Ciarlet–Raviart mixed finite element approximation for an optimal control problem governed by the first biharmonic equation. J. Comput. App. Math. 233.2 (2009), pp. 372–388. doi: 10.1016/j.cam.2009.07.039 P. G. Ciarlet. The finite element method for elliptic problems. Vol. 40. Classics in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia, PA, 2002. doi: 10.1137/1.9780898719208. V. Girault and P.-A. Raviart. Finite element methods for Navier–Stokes equations. Vol. 5. Springer Series in Computational Mathematics. Springer-Verlag, 1986. doi: 10.1007/978-3-642-61623-5 T. Gudi, N. Nataraj, and K. Porwal. An interior penalty method for distributed optimal control problems governed by the biharmonic operator. Comput. Math. App. 68.12 (2014), pp. 2205–2221. doi: 10.1016/j.camwa.2014.08.012 B. P. Lamichhane. A mixed f...