High-order upwind finite volume element method for first-order hyperbolic optimal control problems

Qian Zhang; Jinliang Yan; Zhiyue Zhang

doi:10.21914/anziamj.v57i0.9038

Authors

Qian Zhang School of Mathematical Sciences Nanjing Normal University Nanjing 210023 CHINA http://orcid.org/0000-0001-7855-7958
Jinliang Yan Department of Mathematics and Computer, Wuyi University, Wuyishan http://orcid.org/0000-0003-3672-2358
Zhiyue Zhang School of Mathematical Sciences Nanjing Normal University Nanjing 210023 CHINA http://orcid.org/0000-0001-7070-2532

DOI:

https://doi.org/10.21914/anziamj.v57i0.9038

Keywords:

optimization, variational discretization, high-order upwind finite volume element, hyperbolic optimal control

Abstract

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. doi:10.1017/S1446181116000031

Author Biography

Jinliang Yan, Department of Mathematics and Computer, Wuyi University, Wuyishan

School of Mathematical Sciences Nanjing Normal University Nanjing 210023 CHINA