PreprintCC BY 4.0arXiv
Stability of the P_2 semi-Lagrangian scheme
Abstract
Among the various space interpolation operators used in high-order semi-Lagrangian schemes, the case of finite element interpolation presents a somewhat incomplete stability theory, partly due to the impossibility of applying in a standard form the framework of Von Neumann analysis, even in the constant coefficient case. In this work, the stability of the P_2 semi-Lagrangian scheme is stated in the case of the constant coefficient equation on a uniform mesh, using a suitable extension of the Von Neumann technique to treat block circulant matrices.
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BibTeX
@misc{ferretti2026stability,
title = {{Stability of the P_2 semi-Lagrangian scheme}},
author = {Roberto Ferretti and Michel Mehrenberger},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19806},
eprint = {2610.19806},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19806},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stability of the P_2 semi-Lagrangian scheme
AU - Roberto Ferretti
AU - Michel Mehrenberger
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19806
UR - https://arxiv.org/abs/2610.19806
AB - Among the various space interpolation operators used in high-order semi-Lagrangian schemes, the case of finite element interpolation presents a somewhat incomplete stability theory, partly due to the impossibility of applying in a standard form the framework of Von Neumann analysis, even in the constant coefficient case. In this work, the stability of the P_2 semi-Lagrangian scheme is stated in the case of the constant coefficient equation on a uniform mesh, using a suitable extension of the Von Neumann technique to treat block circulant matrices.
ER -