Convergence analysis for a finite volume evolution Galerkin method for multidimensional hyperbolic systems
Numerical Analysis
2025-11-25 v2 Numerical Analysis
Analysis of PDEs
Abstract
We study the convergence of a finite volume method based on the method of bicharacteristics for multidimensional hyperbolic conservation laws. In particular, we concentrate on the linear wave equation system and nonlinear Euler equations of gas dynamics. We show the stability and the consistency of the numerical approximations. By means of the generalized Lax equivalence principle we prove the convergence of numerical solutions to the strong solution on the lifespan.
Cite
@article{arxiv.2511.00957,
title = {Convergence analysis for a finite volume evolution Galerkin method for multidimensional hyperbolic systems},
author = {Mária Lukáčová-Medvidová and Zhuyan Tang and Yuhuan Yuan},
journal= {arXiv preprint arXiv:2511.00957},
year = {2025}
}