Type
ArticleKAUST Grant Number
CRG4 Award Ref: 2584Date
2019-06-14Preprint Posting Date
2018-02-02Online Publication Date
2019-06-14Print Publication Date
2020-03Permanent link to this record
http://hdl.handle.net/10754/630807
Metadata
Show full item recordAbstract
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/s40072-019-00145-7Sponsors
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 Science and Business Media LLCarXiv
1802.00708Additional Links
http://link.springer.com/10.1007/s40072-019-00145-7ae974a485f413a2113503eed53cd6c53
10.1007/s40072-019-00145-7