On the range diminishing property of numerical schemes for scalar conservation laws

摘要

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. (C) 2020 Elsevier B.V. All rights reserved.