Nous étudions une famille de schémas non linéaires pour l'approximation numérique de l'advection linéaire sur grille quelconque en dimension d'espace supérieure à un. Une preuve de convergence est proposée à partir d'une estimation de la variation longitudinale. Cette estimation est une généralisation multidimensionnelle discrète de l'estimation TVD discrète, bien connue en dimension un d'espace.
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.
Mots-clés : LVD estimate, Harten formalism, linear advection, finite volume methods
@article{M2AN_2001__35_6_1159_0, author = {Despr\'es, Bruno and Lagouti\`ere, Fr\'ed\'eric}, title = {Generalized {Harten} formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {1159--1183}, publisher = {EDP-Sciences}, volume = {35}, number = {6}, year = {2001}, mrnumber = {1873521}, zbl = {1005.76063}, language = {en}, url = {http://archive.numdam.org/item/M2AN_2001__35_6_1159_0/} }
TY - JOUR AU - Després, Bruno AU - Lagoutière, Frédéric TI - Generalized Harten formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2001 SP - 1159 EP - 1183 VL - 35 IS - 6 PB - EDP-Sciences UR - http://archive.numdam.org/item/M2AN_2001__35_6_1159_0/ LA - en ID - M2AN_2001__35_6_1159_0 ER -
%0 Journal Article %A Després, Bruno %A Lagoutière, Frédéric %T Generalized Harten formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids %J ESAIM: Modélisation mathématique et analyse numérique %D 2001 %P 1159-1183 %V 35 %N 6 %I EDP-Sciences %U http://archive.numdam.org/item/M2AN_2001__35_6_1159_0/ %G en %F M2AN_2001__35_6_1159_0
Després, Bruno; Lagoutière, Frédéric. Generalized Harten formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids. ESAIM: Modélisation mathématique et analyse numérique, Tome 35 (2001) no. 6, pp. 1159-1183. http://archive.numdam.org/item/M2AN_2001__35_6_1159_0/
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