【摘要】 本文简要回顾偏微分方程最优控制问题的有限元高精度分析和基于高精度分析的高效有限元算法的若干研究工作,包括椭圆型方程、抛物型方程最优控制问题的有限元超收敛,椭圆型方程、Stokes方程最优控制问题的混合有限元超收敛,以及基于高精度分析的后验误差估计和自适应有限元方法及有限元外推和校正.本文对近年来上述研究进展进行综述,并展望拟开展的研究工作.更多还原

【Abstract】 In this paper, we briefly review the recent advances of superconvergence analysis and related efficient finite element algorithms for PDE-constrained optimal control problems. The emphasis is on the superconvergence of finite element approximations to optimal control problems governed by elliptic and parabolic equations, the superconvergence of mixed finite element approximations to optimal controls of elliptic and Stokes equations,the recovery type a posteriori error estimates and the extrapolation and defect correction methods for optimal controls. We give a survey on the above topics and perspectives for future work are included.更多还原