Generalized Harten formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids

被引：8
作者：
Després, B
Lagoutière, F
机构：
[1] CEA, F-91680 Bruyeres Le Chatel, France
[2] Univ Paris 06, Anal Numer Lab, F-75013 Paris, France
来源：
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2001年 / 35卷 / 06期
关键词：
LVD estimate; Harten formalism; linear advection; finite volume methods;
D O I：
10.1051/m2an:2001152
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study a family of non linear schemes for the numerical solution of linear advection on arbitrary grids in several space dimension. A proof of weak convergence of the family of schemes is given, based on a new Longitudinal Variation Diminishing (LVD) estimate. This estimate is a multidimensional equivalent to the well-known TVD estimate in one dimension. The proof uses a corollary of the Perron-Frobenius theorem applied to a generalized Harten formalism.
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页码：1159 / 1183
页数：25
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