TY - JOUR
T1 - Numerical methods for conservation laws with rough flux
AU - Hoel, H.
AU - Karlsen, K. H.
AU - Risebro, N. H.
AU - Storrøsten, E. B.
N1 - KAUST 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.
PY - 2019/6/14
Y1 - 2019/6/14
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/630807
UR - http://link.springer.com/10.1007/s40072-019-00145-7
UR - http://www.scopus.com/inward/record.url?scp=85068166415&partnerID=8YFLogxK
U2 - 10.1007/s40072-019-00145-7
DO - 10.1007/s40072-019-00145-7
M3 - Article
SN - 2194-0401
VL - 8
SP - 186
EP - 261
JO - Stochastics and Partial Differential Equations: Analysis and Computations
JF - Stochastics and Partial Differential Equations: Analysis and Computations
IS - 1
ER -