Numerical methods for conservation laws with rough flux

Type
Article

Authors
Hoel, H.
Karlsen, K. H.
Risebro, N. H.
Storrøsten, E. B.

KAUST Grant Number
CRG4 Award Ref: 2584

Preprint Posting Date
2018-02-02

Online Publication Date
2019-06-14

Print Publication Date
2020-03

Date
2019-06-14

Abstract
Finite volume methods are proposed for computing approximate pathwise entropy/kinetic solutions to conservation laws with flux functions driven by low-regularity paths. For a convex flux, it is demonstrated that driving path oscillations may lead to “cancellations” in the solution. Making use of this property, we show that for α-Hölder continuous paths the convergence rate of the numerical methods can improve from O(COST -γ) , for some γ∈ [α/ (12 - 8 α) , α/ (10 - 6 α)] , with α∈ (0 , 1) , to O(COST -min(1/4,α/2)). Numerical examples support the theoretical results.

Citation
Hoel, H., Karlsen, K. H., Risebro, N. H., & Storrøsten, E. B. (2019). Numerical methods for conservation laws with rough flux. Stochastics and Partial Differential Equations: Analysis and Computations. doi:10.1007/s40072-019-00145-7

Acknowledgements
This work received supported by the Research Council of Norway through the project Stochastic Conservation Laws (250674/F20) and by the KAUST CRG4 Award Ref: 2584.

Publisher
Springer Nature

Journal
Stochastics and Partial Differential Equations: Analysis and Computations

DOI
10.1007/s40072-019-00145-7

arXiv
1802.00708

Additional Links
http://link.springer.com/10.1007/s40072-019-00145-7

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