AI 中文总结
针对标量守恒律，为全离散单阶段Active Flux方法建立TVD理论，通过适配全变差概念与Harten引理，并高效计算参数，实现三阶方法。研究贡献在于为该高阶方法提供了TVD保证。
AI 中文摘要
针对标量守恒律，为全离散、单阶段Active Flux方法建立了TVD理论。考虑了经典的自由度选择，从而得到三阶方法。从将（离散）全变差概念适配到Active Flux出发，实现了Harten引理的相应适配。最后，为高阶方法赋予参数，这些参数可被高效计算以满足引理条件。
英文摘要
Focusing on scalar conservation laws, a TVD theory is developed for the fully discrete, single-stage Active Flux method. The classical choice of degrees of freedom is considered, yielding a third-order method. Starting from an adaptation of the concept of (discrete) total variation to Active Flux, a corresponding adaptation of Harten's lemma is achieved. Finally, the high-order method is endowed with parameters chosen such that they can be efficiently computed to fulfill the conditions of the lemma.
