Geodesic
Generalized Harten formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 6, pp. 1159-1183

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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.

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.

Classification : 76M12, 65M12
Keywords: LVD estimate, Harten formalism, linear advection, finite volume methods 
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     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: Mathematical Modelling and Numerical Analysis },
     pages = {1159--1183},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {6},
     year = {2001},
     mrnumber = {1873521},
     zbl = {1005.76063},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/M2AN_2001__35_6_1159_0/}
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Després, Bruno; Lagoutière, Frédéric. Generalized Harten formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 6, pp. 1159-1183. http://geodesic.mathdoc.fr/item/M2AN_2001__35_6_1159_0/