TY - JOUR
T1 - Decoupled Mixed Element Methods for Fourth Order Elliptic Optimal Control Problems with Control Constraints
AU - Shen , Yue
AU - Jin , Chang
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 400
EP - 432
PY - 2020
DA - 2020/03
SN - 13
DO - http://doi.org/10.4208/nmtma.OA-2019-0016
UR - https://global-sci.org/intro/article_detail/nmtma/15468.html
KW - Fourth order elliptic equation, optimal control problem, decoupled mixed element method, Lagrange element, nonconforming  Crouzeix-Raviart element, a priori error estimates.
AB - <p style="text-align: justify;">In this paper, we study the finite element methods for distributed optimal control problems governed by the biharmonic operator. Motivated from reducing the regularity of solution space, we use the decoupled mixed element method which was used to approximate the solution of biharmonic equation to solve the fourth order optimal control problems. Two finite element schemes, i.e., Lagrange conforming element combined with full control discretization and the nonconforming Crouzeix-Raviart element combined with variational control discretization, are used to discretize the decoupled optimal control system. The corresponding a priori error estimates are derived under appropriate norms which are then verified by extensive numerical experiments.</p>