Fully Discrete Finite Element Method Based on the Crank-Nicolson Scheme for Parabolic Optimal Control Problem
Aiming at parabolic optimal control problem with integral control constraints,a fully discrete finite element method based on Crank-Nicolson scheme is proposed.The state is discretized by piecewise linear finite elements for the space discretization,Crank-Nicolson scheme for time discretization,and the control variables are approximated by piecewise linear function approximation,so as to obtain a discrete optimal system.The error estimates of state variables,adjoint state variables and control variables are proved,and the theoretical results are verified by numerical examples.
parabolic optimal control problemCrank-Nicolson schemeoptimality system
万方数据
