完全离散P02−P1混合单元的最优控制与抛物方程和低正则性

IF 1.4 Q2 MATHEMATICS, APPLIED

Results in Applied Mathematics Pub Date : 2025-02-01 DOI:10.1016/j.rinam.2025.100551

Yuelong Tang, Yuchun Hua, Yujun Zheng, Chao Wu

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引用次数: 0

摘要

研究了一种求解低正则性抛物型方程最优控制问题的全离散混合方法。采用后向差分格式和P02−P1混合有限元（MFEs）分别对状态和伴随状态进行时间和空间离散化。所有变量的误差估计是通过引入特定的辅助变量和应用适当的正则性假设推导出来的。通过两个算例验证了理论分析的正确性。

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Fully discrete P02−P1 mixed elements for optimal control with parabolic equations and low regularity

This paper studies a novel fully discrete mixed method for optimal control problems (OCPs) with parabolic equations and low regularity. The backward difference scheme and

P_{0}^{2} - P_{1}

mixed finite elements (MFEs) are used for temporal and spatial discretization of state and adjoint state, respectively. Error estimates of all variables are derived through the introduction of specific auxiliary variables and the application of suitable regularity assumptions. The theoretical analysis is validated by two numerical examples.

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来源期刊

Results in Applied Mathematics Mathematics-Applied Mathematics

CiteScore

3.20

自引率

10.00%

发文量

审稿时长

23 days