Error estimates for the implicit MAC scheme for the compressible Navier-Stokes equations

被引：21

作者：

Gallouet, Thierry ^{[1
]}

Maltese, David ^{[2
]}

Novotny, Antonin ^{[2
]}

机构：

[1] Aix Marseille Univ, CNRS, Cent Marseille, I2M,UMR 7373, F-13453 Marseille, France

[2] Univ Toulon & Var, IMATH, EA 2134, BP 20132, F-83957 La Garde, France

来源：

NUMERISCHE MATHEMATIK | 2019年 / 141卷 / 02期

关键词：

FINITE-VOLUME SCHEME; SUITABLE WEAK SOLUTIONS; NUMERICAL APPROXIMATION; FLUID; FLOW; CONVERGENCE; OPERATOR; SYSTEM;

D O I：

10.1007/s00211-018-1007-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove existence of a solution to the implicit MAC scheme for the compressible Navier-Stokes equations. We derive error estimates for this scheme on two and three dimensional Cartesian grids. Error estimates are obtained by using the discrete version of the relative energy method introduced on the continuous level in Feireisl et al. (J Math Fluid Mech 14(4):717-730, 2012). A systematic use of the theoretical continuous analysis of the equations in combination with the numerical tools is crucial for the result. This error estimate does not uses stability hypotheses on the solution of the numerical scheme.

引用

页码：495 / 567

页数：73

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