On convergence of numerical methods for optimization problems governed by scalar hyperbolic conservation laws

Herty，Michael1; Kurganov，Alexander2,3; Kurochkin，Dmitry3

10.1007/978-3-319-91545-6_53

2018

2194-1009

2194-1017

Springer Proceedings in Mathematics and Statistics

236

691-706

Aachen, Germany

Springer New York LLC

We consider optimization problems governed by scalar hyperbolic conservation laws in one space dimension and study numerical schemes for the solution to arising linear adjoint equations. We analyze convergence properties of adjoint and gradient approximations on an unbounded domain x∈ ℝ with a strictly convex flux. This paper provides the theoretical foundation of the scheme introduced in (Herty, Kurganov and Kurochkin, Commun. Math. Sci. 51, 15–48 (2015)) [14]. We also demonstrate that using a higher order temporal discretization helps to substantially improve both the efficiency and accuracy of the overall numerical method.

其他

英语

EI

[DMS-1107444] ; [HE5386/13,14,15-1] ; [EXC128] ; National Science Foundation[DMS-1115718] ; National Science Foundation[DMS-1521009]

20182705519515

Computational mechanics ; Optimization ; Physical properties

Mathematics:921 ; Physical Properties of Gases, Liquids and Solids:931.2

2-s2.0-85049362021

Scopus

1.,Department of Mathematics,RWTH Aachen University,Aachen,Templergraben 55,D-52056,Germany
2.,Department of Mathematics,Southern University of Science and Technology of China,Shenzhen,518055,China
3.,Mathematics Department,Tulane University,New Orleans,70118,United States

Herty，Michael,Kurganov，Alexander,Kurochkin，Dmitry. On convergence of numerical methods for optimization problems governed by scalar hyperbolic conservation laws[C]:Springer New York LLC,2018:691-706.