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

Qian Zhang, Jinliang Yan, Zhiyue Zhang

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

Keywords


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



DOI: http://dx.doi.org/10.21914/anziamj.v57i0.9038



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.