A convergence result for finite volume schemes on riemannian manifolds
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 5, pp. 929-955.

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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 : 10.1051/m2an/2009013
Classification : 74S10, 35L65, 58J45
Mots-clés : finite volume method, conservation law, curved manifold
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     title = {A convergence result for finite volume schemes on riemannian manifolds},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {929--955},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {5},
     year = {2009},
     doi = {10.1051/m2an/2009013},
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     language = {en},
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Giesselmann, Jan. A convergence result for finite volume schemes on riemannian manifolds. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 5, pp. 929-955. doi : 10.1051/m2an/2009013. https://geodesic-test.mathdoc.fr/articles/10.1051/m2an/2009013/

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