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

Bruno Després; Frédéric Lagoutière

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2001)

  • Volume: 35, Issue: 6, page 1159-1183
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Després, Bruno, and Lagoutière, Frédéric. "Generalized Harten formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.6 (2001): 1159-1183. <http://eudml.org/doc/194090>.

@article{Després2001,
abstract = {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.},
author = {Després, Bruno, Lagoutière, Frédéric},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {LVD estimate; Harten formalism; linear advection; finite volume methods; weak convergence; longitudinal variation diminishing estimate; finite volume method; Perron-Frobenius theorem; generalized Harten formalism},
language = {eng},
number = {6},
pages = {1159-1183},
publisher = {EDP-Sciences},
title = {Generalized Harten formalism and longitudinal variation diminishing schemes for linear advection on arbitrary grids},
url = {http://eudml.org/doc/194090},
volume = {35},
year = {2001},
}

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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2001
PB - EDP-Sciences
VL - 35
IS - 6
SP - 1159
EP - 1183
AB - 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.
LA - eng
KW - LVD estimate; Harten formalism; linear advection; finite volume methods; weak convergence; longitudinal variation diminishing estimate; finite volume method; Perron-Frobenius theorem; generalized Harten formalism
UR - http://eudml.org/doc/194090
ER -

References

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