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

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 P02−P1 mixed finite elements (MFEs) are used for temporal and spatial discretization of state and adjoint state, respectively. Er...

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Bibliographic Details
Main Authors: Yuelong Tang, Yuchun Hua, Yujun Zheng, Chao Wu
Format: Article
Language:English
Published: Elsevier 2025-02-01
Series:Results in Applied Mathematics
Subjects:
Error analysis
P20 −P1 mixed elements
Low regularity
Optimal control problems
Online Access:http://www.sciencedirect.com/science/article/pii/S2590037425000159
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Summary: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 P02−P1 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.
ISSN:2590-0374

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