Error analysis of a Euler finite element scheme for Natural convection model with variable density
Numerical Analysis
2025-05-20 v2 Numerical Analysis
Abstract
In this paper, we derive first-order Euler finite element discretization schemes for a time-dependent natural convection model with variable density (NCVD). The model is governed by the variable density Navier-Stokes equations coupled with a parabolic partial differential equation that describes the evolution of temperature. Stability and error estimate for the velocity, pressure, density and temperature in -norm are proved by using finite element approximations in space and finite differences in time. Finally, the numerical results are showed to support the theoretical analysis.
Cite
@article{arxiv.2504.04381,
title = {Error analysis of a Euler finite element scheme for Natural convection model with variable density},
author = {Li Hang and Chenyang Li},
journal= {arXiv preprint arXiv:2504.04381},
year = {2025}
}