非线性抛物最优控制问题插值系数混合有限元解的先验误差估计

采用插值系数的思想去处理方程中的非线性项,建立了非线性抛物最优控制问题插值系数混合有限元的离散格式,对状态方程和对偶状态方程利用最低阶的Raviart-Thomas混合有限元逼近,控制变量利用分片常函数逼近,应用一些偏微分方程混合有限元的误差估计结果,得到状态变量和控制变量逼近解的最优阶先验误差估计.

A priori error estimate of interpolation coefficients based on mixed finite element solutions for nonlinear parabolic optimal control problems

In this paper,we have extended the excellent idea of interpolation coefficients for nonlinear parabolic optimal control problems,that is,the mixed finite element methods. By using the interpolation coefficient thought to process the nonlinear term of equations,we have presented the mixed finite element approximation with interpolated coefficients for nonlinear parabolic optimal control problems. We have investigated a priori error estimate of quadratic convex optimal control problems governed by nonlinear parabolic equations by using interpolation coefficients based on finite element methods. The state and the co-state are approximated by the lowest order Raviart-Thomas with finite element spaces and the control is approximated by piecewise constant functions. By applying some results of error estimates of mixed finite element methods for partial differential equations,we have derived a priori error estimate of optimal order both for the coupled state and the approximation of control variables of the optimal control problem.