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

Feireisl Eduard; Lukacova-Medvidova Maria; She Bangwei

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

机译：改进了可压缩 Navier-Stokes 系统的有限体积和 MAC 方案的误差估计

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摘要

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.

机译：我们提出了应用于可压缩Navier-Stokes方程的有限体积和有限差分方法的新误差估计。改进的误差估计的主要创新成分是精细的一致性分析与相对能量不等式的连续版本相结合。因此，我们获得了比迄今为止文献中更好的收敛率。此外，误差估计值在绝热系数的整个物理相关范围内成立。

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来源
《Numerische Mathematik》 |2023年第3期|493-529|共37页
作者
Feireisl Eduard; Lukacova-Medvidova Maria; She Bangwei;
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作者单位

Acad Sci Czech Republic;

Capital Normal Univ;

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原文格式 PDF
正文语种英语
中图分类数值分析;
关键词
35Q30; 65N12; 76M12; 76M20; DIFFERENCE SCHEME; ELEMENT-METHOD; CONVERGENCE; EQUATIONS;

机译：35Q30;65N12;76分12秒;76分20秒;差异方案;元素方法;收敛;方程;

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1. Convergence of a Mixed Finite Element-Finite Volume Scheme for the Isentropic Navier-Stokes System via Dissipative Measure-Valued Solutions [J] . Feireisl Eduard, Lukacova-Medvidova Maria Foundations of computational mathematics . 2018,第3期

机译：Convergence of a Mixed Finite Element-Finite Volume Scheme for the Isentropic Navier-Stokes System via Dissipative Measure-Valued Solutions
2. Convergence and Error Estimates of a Mixed Discontinuous Galerkin-Finite Element Method for the Semi-stationary Compressible Stokes System [J] . Shipeng Mao, Wendong Xue Journal of scientific computing . 2023,第3期

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3. Compressible Navier-Stokes Equations with Potential Temperature Transport: Stability of the Strong Solution and Numerical Error Estimates [J] . Lukacova-Medvidova Maria, Schomer Andreas Journal of mathematical fluid mechanics . 2023,第1期

机译：Compressible Navier-Stokes Equations with Potential Temperature Transport: Stability of the Strong Solution and Numerical Error Estimates

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

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