PreprintCC BY-NC-SA 4.0HAL
A TVD Active Flux method for scalar conservation laws
Abstract
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.
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BibTeX
@misc{barsukow2026active,
title = {{A TVD Active Flux method for scalar conservation laws}},
author = {Wasilij Barsukow},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05920},
eprint = {2610.05920},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05794428v1},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - A TVD Active Flux method for scalar conservation laws
AU - Wasilij Barsukow
PY - 2026
DA - 2026/10/05
PB - HAL
DO - 10.48550/arxiv.2610.05920
UR - https://hal.science/hal-05794428v1
AB - 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.
ER -