论文标题
分布式最佳控制问题不连续的盖金方法，该方法由时间分数扩散方程控制
Discontinuous Galerkin method for a distributed optimal control problem governed by a time fractional diffusion equation
论文作者
论文摘要
本文致力于对控制受约束的分布式最佳控制问题的数值分析，但具有时间分数扩散方程，并具有非平滑的初始数据。状态和联合国家的解决方案分解为单数和常规部分，并获得了单个零件的一些增长估计。遵循变分离散概念，通过在空间中使用线性符合有限元法和分段恒定不连续的盖尔金方法，将完全离散化应用于相应的状态和共同状态方程。通过增长估计，使用非平滑初始数据得出错误估计。特别是，分级的时间网格用于获得一阶时间准确性。最后，进行数值实验以验证理论结果。
This paper is devoted to the numerical analysis of a control constrained distributed optimal control problem subject to a time fractional diffusion equation with non-smooth initial data. The solutions of state and co-state are decomposed into singular and regular parts, and some growth estimates are obtained for the singular parts. Following the variational discretization concept, a full discretization is applied to the corresponding state and co-state equations by using linear conforming finite element method in space and piecewise constant discontinuous Galerkin method in time. By the growth estimates, error estimates are derived with non-smooth initial data. In particular, graded temporal grids are used to obtain the first-order temporal accuracy. Finally, numerical experiments are performed to verify the theoretical results.
