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 \(\alpha \)-Hölder continuous 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 \(\mathcal {O}(\text {COST}^{-\min (1/4,\alpha /2)})\). Numerical examples support the theoretical results.

中文翻译：

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粗糙通量守恒律的数值方法

提出了有限体积方法，用于计算由低规则性路径驱动的通量函数的守恒律的近似路径熵/动力学解。对于凸通量，证明了驱动路径的振动可能导致溶液中的“取消”。利用此属性，我们表明对于\（\ alpha \）- Hölder连续路径，数值方法的收敛速度可以从\（\ mathcal {O}（\ text {COST} ^ {-\ gamma}）改进\） ，对于一些\（\伽马\在\左[\的α/（12-8 \阿尔法），\的α/（10-6 \阿尔法）\右] \） ，用\（\阿尔法\在（0 ，1）\）到\（\ mathcal {O}（\ text {COST} ^ {-\ min（1/4，\ alpha / 2）}）\）。数值例子支持了理论结果。