A convergence result for finite volume schemes on riemannian manifolds

Giesselmann, Jan

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 43 (2009), p. 929-955 / Harvested from Numdam

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Résumé

This paper studies a family of finite volume schemes for the hyperbolic scalar conservation law $u_{t} + \nabla_{g} \cdot f (x, u) = 0$ on a closed riemannian manifold $M .$ For an initial value in BV( $M$ ) we will show that these schemes converge with a $h^{\frac{1}{4}}$ convergence rate towards the entropy solution. When $M$ is $1$ -dimensional the schemes are TVD and we will show that this improves the convergence rate to $h^{\frac{1}{2}} .$

Publié le : 2009-01-01

MR 2559739 | Zbl 1173.74454

DOI : https://doi.org/10.1051/m2an/2009013
Classification: 74S10, 35L65, 58J45

@article{M2AN_2009__43_5_929_0,
     author = {Giesselmann, Jan},
     title = {A convergence result for finite volume schemes on riemannian manifolds},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {43},
     year = {2009},
     pages = {929-955},
     doi = {10.1051/m2an/2009013},
     mrnumber = {2559739},
     zbl = {1173.74454},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2009__43_5_929_0}
}

Giesselmann, Jan. A convergence result for finite volume schemes on riemannian manifolds. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 43 (2009) pp. 929-955. doi : 10.1051/m2an/2009013. http://gdmltest.u-ga.fr/item/M2AN_2009__43_5_929_0/

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