Exact solutions of scalar conservation laws have the property that maxima are non-increasing, minima are non-decreasing and no new extrema are created. We present a simple and reliable general condition for numerical schemes to mimic this property. We demonstrate the result by applying it to various schemes, which leads to various CFL-like conditions.

中文翻译：

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标量守恒律数值格式的范围递减性质

标量守恒定律的精确解具有以下性质：最大值不增加，最小值不减小，并且不创建新的极值。我们为数值方案提供了一个简单可靠的通用条件，以模仿该特性。我们通过将其应用于各种方案来证明结果，这会导致各种类似于CFL的情况。