论文标题
前跟踪方法的不连续通量和收敛速率的保护法的通量稳定性
Flux-stability for conservation laws with discontinuous flux and convergence rates of the front tracking method
论文作者
论文摘要
我们证明，在通量的变化中，标量保护定律的适应性熵解决方案在通量的变化方面是稳定的。我们使用此稳定性结果证明了前跟踪方法的收敛速率 - 一种数值方法，在不连续通量的保护定律领域中广泛使用。据我们所知，这两种结果都是关于不连续的保存法律文献中的第一个结果。我们还提出了数值实验，以验证收敛速率结果并比较使用前跟踪方法计算的数值解决方案与有限体积近似值。
We prove that adapted entropy solutions of scalar conservation laws with discontinuous flux are stable with respect to changes in the flux under the assumption that the flux is strictly monotone in u and the spatial dependency is piecewise constant with finitely many discontinuities. We use this stability result to prove a convergence rate for the front tracking method -- a numerical method which is widely used in the field of conservation laws with discontinuous flux. To the best of our knowledge, both of these results are the first of their kind in the literature on conservation laws with discontinuous flux. We also present numerical experiments verifying the convergence rate results and comparing numerical solutions computed with the front tracking method to finite volume approximations.
