Multipoint flux mixed finite element method for parabolic optimal control problems

In this paper, we research semi-discrete multipoint flux mixed finite element (MFMFE) method for parabolic optimal control problem (OCP). The state and co-state variables are approximated by the lowest order Brezzi-Douglas-Marini (BDM) mixed finite element (MFE) spaces and the control is approximated by piecewise constant. The advantage of this type of mixed element method is that it can decouple the state and adjoint state variables as cell-centered difference schemes rather than to solve saddle point algebraic equations. Error estimates and convergence orders are derived rigorously for state and control variables. Finally, a numerical example is given to confirm our theoretical analysis.

Automated summary

This paper investigates the application of the semi-discrete multipoint flux mixed finite element method for parabolic optimal control problems, approximating the state and control variables to solve the problem. The advantage lies in decoupling the state and adjoint state variables, obtaining convergence orders and error estimates.