Improved error estimates for the finite volume and the MAC schemes for the compressible Navier-Stokes system

2022/05/09 by Eduard Feireisl, Feireisl, Eduard, Mária Lukáčová-Medviďová +3 · 1 citation
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2205.04076

openalex publication_date 2022/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present new error estimates for the finite volume and finite difference methods applied to the compressible Navier-Stokes equations. The main innovative ingredients of the improved error estimates are a refined consistency analysis combined with a continuous version of the relative energy inequality. Consequently, we obtain better convergence rates than those available in the literature so far. Moreover, the error estimates hold in the whole physically relevant range of the adiabatic coefficient.

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• Error analysis of an asymptotic-preserving, energy-stable finite volume method for barotropic Euler equations

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