标题： 主动通量方法在求和-分部算子框架中的稳定性 显示英文标题

标题： Stability of the Active Flux Method in the Framework of Summation-by-Parts Operators

摘要： 主动通量方法是一种用于守恒定律的数值方法，结合了单元平均值和点值，基于有限体积法和有限差分法的思想。这种不寻常的组合已被证明在许多情况下效果良好。我们通过从求和-分部（SBP）算子的角度分析，扩展了主动通量方法的理论依据，这些算子通常用于分析有限差分、有限体积和有限元方案。我们表明，主动通量方法可以使用退化的SBP算子进行表述，从而为展示主动通量方法的能量稳定性提供了一种首次且新颖的方法。 显示英文摘要

摘要： The Active Flux method is a numerical method for conservation laws using a combination of cell averages and point values, based on ideas from finite volumes and finite differences. This unusual mix has been shown to work well in many situations. We expand the theoretical justifications of the Active Flux method by analyzing it from the point of view of summation-by-parts (SBP) operators, which are routinely used to analyze finite difference, finite volume, and finite element schemes. We show that the Active Flux method can be formulated using degenerate SBP operators, yielding a first and novel approach for showing the energy stability of the Active Flux method.