{"paper":{"title":"Numerical methods for conservation laws with rough flux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Erlend Briseid Storr{\\o}sten, H{\\aa}kon Hoel, Kenneth Hvistendahl Karlsen, Nils Henrik Risebro","submitted_at":"2018-02-02T14:54:22Z","abstract_excerpt":"Finite volume methods are proposed for computing approximate pathwise entropy/kinetic solutions to conservation laws with a rough path dependent flux function. For a convex flux, it is demonstrated that rough path oscillations may lead to \"cancellations\" in the solution. Making use of this property, we show that for $\\alpha$-H{\\\"o}lder continuous rough paths the convergence rate of the numerical methods can improve from $\\mathcal{O}(\\text{COST}^{-\\gamma})$, for some $\\gamma \\in \\left[\\alpha/(12-8\\alpha), \\alpha/(10-6\\alpha)\\right]$, with $\\alpha\\in (0, 1)$, to $\\mathcal{O}(\\text{COST}^{-\\min(1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00708","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}