A convergence result for finite volume schemes on riemannian manifolds
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 5, p. 929-955

This paper studies a family of finite volume schemes for the hyperbolic scalar conservation law u t + g ·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 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 1 2 .

DOI : https://doi.org/10.1051/m2an/2009013
Classification:  74S10,  35L65,  58J45
Keywords: finite volume method, conservation law, curved manifold
@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},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {5},
     year = {2009},
     pages = {929-955},
     doi = {10.1051/m2an/2009013},
     zbl = {1173.74454},
     mrnumber = {2559739},
     language = {en},
     url = {http://www.numdam.org/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, Volume 43 (2009) no. 5, pp. 929-955. doi : 10.1051/m2an/2009013. http://www.numdam.org/item/M2AN_2009__43_5_929_0/

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