Numerical methods for conservation laws with rough flux

H. Hoel, K. H. Karlsen, N. H. Risebro, E. B. Storrøsten

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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 languageEnglish (US)
Pages (from-to)186-261
Number of pages76
JournalStochastics and Partial Differential Equations: Analysis and Computations
Volume8
Issue number1
DOIs
StatePublished - Jun 14 2019
Externally publishedYes

Fingerprint Dive into the research topics of 'Numerical methods for conservation laws with rough flux'. Together they form a unique fingerprint.

Cite this