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arXiv · 2504.04381

Error analysis of a Euler finite element scheme for Natural convection model with variable density

Li Hang·Chenyang Li
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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 $L^2$-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.

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Li Hang, Chenyang Li. 2025-04-06. Error analysis of a Euler finite element scheme for Natural convection model with variable density. https://arxiv.org/abs/2504.04381

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