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HIGH-ORDER UPWIND FINITE VOLUME ELEMENT METHOD FOR FIRST-ORDER HYPERBOLIC OPTIMAL CONTROL PROBLEMS

Part of: Optimality conditions Existence theories Partial differential equations, boundary value problems

Published online by Cambridge University Press:  11 April 2016

QIAN ZHANG Open the ORCID record for QIAN ZHANG [Opens in a new window] ,
JINLIANG YAN Open the ORCID record for JINLIANG YAN [Opens in a new window]  and
ZHIYUE ZHANG Open the ORCID record for ZHIYUE ZHANG [Opens in a new window]
QIAN ZHANG
Affiliation:
School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210023, China email zhangqian7452019@126.com, zhangzhiyue@njnu.edu.cn
JINLIANG YAN
Affiliation:
Department of Mathematics and Computer, Wuyi University, Wuyishan 354300, China email yanjinliang3333@163.com
ZHIYUE ZHANG*
Affiliation:
School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210023, China email zhangqian7452019@126.com, zhangzhiyue@njnu.edu.cn
*
✉zhangzhiyue@njnu.edu.cn
Rights & Permissions [Opens in a new window]

Abstract

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We present a high-order upwind finite volume element method to solve optimal control problems governed by first-order hyperbolic equations. The method is efficient and easy for implementation. Both the semi-discrete error estimates and the fully discrete error estimates are derived. Optimal order error estimates in the sense of $L^{2}$-norm are obtained. Numerical examples are provided to confirm the effectiveness of the method and the theoretical results.

Keywords

optimizationvariational discretizationhigh-order upwind finite volume elementhyperbolic optimal control

MSC classification

Primary: 65N15: Error bounds
Secondary: 49K20: Problems involving partial differential equations 49J20: Optimal control problems involving partial differential equations 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
The ANZIAM Journal , Volume 57 , Issue 4 , April 2016 , pp. 482 - 498
Copyright
© 2016 Australian Mathematical Society 

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