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research article
Numerical methods for conservation laws with rough flux
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 alpha-Holder continuous paths the convergence rate of the numerical methods can improve from O(COST-gamma), for some gamma is an element of [alpha/(12 - 8 alpha), alpha/(10 - 6 alpha)], with alpha is an element of (0, 1), to O(COST-min(1/4,alpha/2)). Numerical examples support the theoretical results.
Use this identifier to reference this record
Type
research article
Web of Science ID
WOS:000514663400005
Authors
Publication date
2020-03-01
Volume
8
Issue
1
Start page
186
End page
261
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
March 5, 2020