A CONVERGENCE RESULT FOR FINITE VOLUME SCHEMES ON RIEMANNIAN MANIFOLDS

被引：11
作者：
Giesselmann, Jan [1 ]
机构：
[1] Univ Stuttgart IANS, D-70569 Stuttgart, Germany
来源：
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2009年 / 43卷 / 05期
关键词：
Finite volume method; conservation law; curved manifold; SHALLOW-WATER TURBULENCE; SPHERICAL GEOMETRY; HYPERBOLIC SYSTEMS; SOLAR TACHOCLINE; GALERKIN METHODS; EQUATIONS; PROPAGATION; WAVES; GRIDS; JETS;
D O I：
10.1051/m2an/2009013
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper studies a family of finite volume schemes for the hyperbolic scalar conservation law u(t) + del(g) . f( x, u) = 0 on a closed Riemannian manifold M. For an initial value in BV( M) we will show that these schemes converge with a h 1/4 convergence rate towards the entropy solution. When M is 1-dimensional the schemes are TVD and we will show that this improves the convergence rate to h 1/2.
引用
收藏
页码：929 / 955
页数：27
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