Convergence analysis of a MAC scheme for the barotropic Euler system
Numerical Analysis
2026-07-06 v1
Abstract
We study a Marker-and-Cell (MAC) scheme for the barotropic Euler system. First, we apply the recently developed Lax-type convergence theorem to show the convergence of the MAC scheme to i) a dissipative weak solution unconditionally and ii) a strong solution as long as it exists. Second, We derive relative energy error estimates up to the lifespan of a strong solution, without assuming uniform boundedness of the numerical sequence. Additionally, assuming the boundedness of the numerical solutions, we obtain the optimal relative energy rate of 1, corresponding to a convergence rate of 1/2 for the numerical solutions. Finally, we corroborate our theoretical results by numerical experiments.
Cite
@article{arxiv.2607.05105,
title = {Convergence analysis of a MAC scheme for the barotropic Euler system},
author = {Bangwei She and Congying Wang and Jin Zhao},
journal= {arXiv preprint arXiv:2607.05105},
year = {2026}
}