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.
|Original language||English (US)|
|Number of pages||76|
|Journal||Stochastics and Partial Differential Equations: Analysis and Computations|
|State||Published - Jun 14 2019|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): CRG4 Award Ref: 2584
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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.