PreprintCC BY-NC-SA 4.0HAL
Parabolic CFL restriction of a genuine second-order1 entropy-stable scheme for scalar hyperbolic2 equations
Abstract
This work concerns the second-order accurate spatial numerical approximations of the weak solutions of scalar hyperbolic conservation laws. After a recent paper that gives a circumvention of the barrier theorems for such approximations, this work establishes a local fully discrete entropy inequality under an explicit parabolic CFL restriction. This result also leads to an efficient implementation of a genuine second-order scheme that is illustrated with numerical experiments.
Related
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- Time derivative estimates for normalized parabolic p-Laplace equations
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- Global Hölder solvability for parabolic equations with interior Morrey data
BibTeX
@misc{berthon2026parabolic,
title = {{Parabolic CFL restriction of a genuine second-order1 entropy-stable scheme for scalar hyperbolic2 equations}},
author = {Christophe Berthon and Ludovic Martaud},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05741680v1},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Parabolic CFL restriction of a genuine second-order1 entropy-stable scheme for scalar hyperbolic2 equations
AU - Christophe Berthon
AU - Ludovic Martaud
PY - 2026
DA - 2026/09/08
PB - HAL
UR - https://hal.science/hal-05741680v1
AB - This work concerns the second-order accurate spatial numerical approximations of the weak solutions of scalar hyperbolic conservation laws. After a recent paper that gives a circumvention of the barrier theorems for such approximations, this work establishes a local fully discrete entropy inequality under an explicit parabolic CFL restriction. This result also leads to an efficient implementation of a genuine second-order scheme that is illustrated with numerical experiments.
ER -