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finite volume methods.

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Generalized Harten Formalism and Longitudinal Variation Diminishing schemes for Linear Advection on Arbitrary Grids
Bruno Després, Frédéric Lagoutière
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 35 / Issue 6 / November 2001

Published online by Cambridge University Press:

15 April 2002, pp. 1159-1183

Print publication:

November 2001
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We study a family of non linear schemes for the numerical solution oflinear 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.