Year: 2025
Type: article
Abstract: WENO schemes are high order accurate shock capturing methods for hyperbolic conservation laws. In this paper theoretical stability properties are presented. In fact, we prove, assuming some reasonable hypotheses from a practical point of view, that the numerical flux is Lipschitz continuous and that the $$TV(u^n)$$ T V ( u n ) is uniformly bounded for all n, k with $$k k < k 0 , $$nk\le T$$ n k ≤ T . Both results give the two sufficient properties used in the convergence framework presented in Leveque (Numerical methods for conservation laws. Birkhäuser Verlag (Lectures in Mathematics), 1990).
Source: The Journal of Analysis
Authors: Sergio Amat, Sonia Busquier, Juan Ruiz
Institution: Universidad Politécnica de Cartagena
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,090
OpenAlex ID: W4409487135