一类非线性抛物最优控制问题的Crank-Nicolson有限元近似格式误差分析
Error Estimate for the Crank-Nicolson Finite Element Scheme Approximation of Nonlinear Parabolic Optimal Control Problems
DOI: 10.12677/ORF.2023.134415, PDF,    国家自然科学基金支持
作者: 丁美玲, 李欢欢, 罗贤兵*：贵州大学数学与统计学院，贵州 贵阳
关键词: 非线性；抛物最优控制；Crank-Nicolson 格式；先验误差估计；有限元；Nonlinear； Parabolic Optimal Control； Crank-Nicolson Scheme； Priori Error Estimates； Finite Element
摘要: 本文对一类非线性抛物最优控制问题给出了Crank-Nicolson有限元近似格式。对于状态y和伴随状态变量p采用线性协调有限元离散，对控制变量u采用分片常数近似；得到了控制和状态变量近似的先验误差估计O(h + hu + (∆t)2)，为验证算法的有效性给出了数值算例。
Abstract: In this paper, we present a Crank − Nicolson scheme combined with finite element approximation for a class of nonlinear parabolic optimal control problems, where the state y and co-state p are discretized by picewise linear continuous function and the control u is approximations by picewise constant functions. Numerical experiments verify that the convergence order is O(h + hU + (∆t)2).
文章引用：丁美玲, 李欢欢, 罗贤兵. 一类非线性抛物最优控制问题的Crank-Nicolson有限元近似格式误差分析[J]. 运筹与模糊学, 2023, 13(4): 4147-4166. https://doi.org/10.12677/ORF.2023.134415

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