In this paper, we propose a Galerkin finite element method for the elliptic optimal control problem governed by the Riesz space-fractional PDEs on 2D domains with control variable being discretized by variational discretization technique. The optimality condition is derived and priori error estimates of control, costate and state variables are successfully established. Numerical test is carried out to illustrate the accuracy performance of this approach.

翻译：在本文中,我们建议对由Riesz空间中断裂式PDEs在2D域上管辖的椭圆顶最佳控制问题采用Galerkin有限要素方法,控制变量通过可变离散技术分离,最佳性条件得到推导,对控制、成本和状态变量的先验性误差估计得到成功确定,进行了数值测试,以说明这一方法的准确性。