The Research Of Mixed Finite Element Method For Nonlinear Optimal Control Problems

Regarding to the nonlinear optimal control problem, in this dissertation, we study themixed interpolation coefficient finite element method, obtain a simple and efficientcomputing scheme for a class of nonlinear optimal control problem and give thecorresponding error analysis by using the interpolation coefficient of nonlinear term. It alsoexpands the mixed interpolation coefficient finite element method which aims at researchingand calculating optimal control problem.There are two parts in this paper. In the first part, we study the order k mixed finiteelement method of one-dimensional nonlinear elliptic optimal control problem and obtain thecalculation scheme by using the interpolation coefficient mixed finite element method todiscrete. And we give the priori error estimation and analysis the given theory throughNumerical experimentsIn the second part, as to the numerical calculation of two-dimensional nonlinear optimalcontrol problem, we research the order k interpolation coefficient Raviart-Thomas mixedfinite element method on the basis of quasi-uniform triangle. Meanwhile, it applies twoapproaches to discuss the interpolation coefficient mixed finite element and derive their priorierror estimations.