Generalized Harten Formalism and Longitudinal Variation Diminishing schemes for Linear Advection on Arbitrary Grids

Bruno Després; Frédéric Lagoutière

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • 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 35.6 (2010): 1159-1183. <http://eudml.org/doc/197495>.

@article{Després2010,
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},
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},
month = {3},
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/197495},
volume = {35},
year = {2010},
}

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
DA - 2010/3//
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/197495
ER -

References

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