ERROR ESTIMATE FOR TIME-EXPLICIT FINITE VOLUME APPROXIMATION OF STRONG SOLUTIONS TO SYSTEMS OF CONSERVATION LAWS

被引：6

作者：

Cances, Clement ^{[1
]}

Mathis, Helene ^{[2
]}

Seguin, Nicolas ^{[2
]}

机构：

[1] Inria Lille Nord Europe, Team RAPSODI, F-59650 Villeneuve Dascq, France

[2] Univ Nantes, Lab Math Jean Leray, F-44322 Nantes 03, France

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2016年 / 54卷 / 02期

关键词：

hyperbolic systems; finite volume scheme; relative entropy; error estimate; NONLINEAR HYPERBOLIC EQUATION; RELATIVE ENTROPY; KINETIC-EQUATIONS; GLOBAL EXISTENCE; GAS-DYNAMICS; A-PRIORI; SCHEMES; CONVERGENCE; LIMITS;

D O I：

10.1137/15M1029886

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the finite volume approximation of strong solutions to nonlinear systems of conservation laws. We focus on time-explicit schemes on unstructured meshes, with entropy satisfying numerical fluxes. The numerical entropy dissipation is quantified at each interface of the mesh, which enables us to prove a weak-BV estimate for the numerical approximation under a strengthened CFL condition. Then we derive error estimates in the multidimensional case, using the relative entropy between the strong solution and its finite volume approximation. The error terms are carefully studied, leading to a classical O(h(1/4)) estimate in L-2 under this strengthened CFL condition.

引用

页码：1263 / 1287

页数：25

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