Convergence analysis for a finite-volume scheme for the Euler- and Navier-Stokes-Korteweg system via energy-variational solutions
Numerical Analysis
2026-04-01 v1 Numerical Analysis
Analysis of PDEs
Abstract
We consider a structure-preserving finite-volume scheme for the Euler-Korteweg (EK) and Navier-Stokes-Korteweg (NSK) equations. We prove that its numerical solutions converge to energy-variational solutions of EK or NSK under mesh refinement. Energy-variational solutions constitute a novel solution concept that has recently been introduced for hyperbolic conservation laws, including the EK system, and which we extend to the NSK model. Our proof is based on establishing uniform estimates following from the properties of the structure-preserving scheme, and using the stability of the energy-variational formulation under weak convergence in the natural energy spaces.
Keywords
Cite
@article{arxiv.2603.29880,
title = {Convergence analysis for a finite-volume scheme for the Euler- and Navier-Stokes-Korteweg system via energy-variational solutions},
author = {Thomas Eiter and Jan Giesselmann and Robert Lasarzik and Philipp Öffner and Robert Sauerborn},
journal= {arXiv preprint arXiv:2603.29880},
year = {2026}
}