KAUST Grant NumberCRG4 Award Ref: 2584
Preprint Posting Date2018-02-02
Online Publication Date2019-06-14
Print Publication Date2020-03
Permanent link to this recordhttp://hdl.handle.net/10754/630807
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AbstractFinite 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.
CitationHoel, 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
SponsorsThis 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.