摘要
利用插值系数混合有限元方法求解半线性最优控制问题,采用插值系数的思想去处理方程中的非线性项,建立了半线性椭圆最优控制问题插值系数混合有限元的离散格式,将状态方程和对偶状态方程利用低阶的Raviart-Thomas混合有限元空间离散,控制变量利用分片常函数逼近,最后获得状态变量和控制变量的L2范数和H(div)范数的最优阶先验误差估计.
In this paper,the authors extend the excellent idea of interpolation coefficients for semilinear optimal control problems to the mixed finite element methods. By using the interpolation coefficients thought to process the nonlinear term of equations ,we present the mixed finite element approximation with interpolation coefficients for general optimal control problems governed by semilinear elliptic equations. The state and the co-state are discretized by the lowest order Raviart-Thomas mixed finite element space and the control is discretized by piecewise constant elements. We derive a priori error estimates in L2 norm and H （div） norm for the coupled state and control variables with optimal convergence order h2.
出处
《怀化学院学报》
2016年第11期21-26,共6页
Journal of Huaihua University
基金
国家自然科学基金(11201510
11171251)
中国博士后科学基金(2015M580197)
重庆市科委项目(cstc 2015jcyj A20001)
教育部春晖计划(Z2015139)
关键词
半线性椭圆
最优控制问题
插值系数混合有限元解
先验误差估计
semilinear elliptic
optimal control problems
solutions
priori error estimatesinterpolation coefficients mixed finite element
