Convergence and proposed optimality of adaptive finite element methods for nonlinear optimal control problems-Reference-Cited by-同舟云学术

Convergence and proposed optimality of adaptive finite element methods for nonlinear optimal control problems

Published:2022 Issue:11 Volume:7 Page:19664-19695
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Lu Zuliang¹²,Cai Fei¹,Xu Ruixiang¹,Xing Lu¹

Affiliation:

1. Key Laboratory for Nonlinear Science and System Structure, Chongqing Three Gorges University, Chongqing 404000, China

2. Research Center for Mathematics and Economics, Tianjin University of Finance and Economics, Tianjin 300222, China

Abstract

<abstract><p>This paper investigates the adaptive finite element method for nonlinear optimal control problem, and the research content of reference (<sup>[<xref ref-type="bibr" rid="b21">21</xref>]</sup> H. Leng and Y. Chen, 2017) is extended accordingly. Linear discretisation of the equation of state and the equation of common state is performed using continuous segmentation functions. At the same time, we use the bubble function technique to prove that the posterior error estimates are obtained from the upper and lower bounds. What is more, for the adaptive finite element method, we also consider convergence and quasi-optimality, where we find that the demand $ h_0\ll 1 $ on the initial grid is unconstrained for the convergence analysis of the proposed adaptive algorithm for the nonlinear optimal control problem. Simultaneously, some numerical simulation is used to verify our theoretical analysis.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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