Volume 43, Number 5, September-October 2009
|Page(s)||929 - 955|
|Published online||12 June 2009|
A convergence result for finite volume schemes on Riemannian manifolds
Universität Stuttgart (IANS), Pfaffenwaldring 57, 70569 Stuttgart, Germany. email@example.com
Revised: 24 November 2008
This paper studies a family of finite volume schemes for the hyperbolic scalar conservation law on a closed Riemannian manifold M. For an initial value in BV(M) we will show that these schemes converge with a 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
Mathematics Subject Classification: 74S10 / 35L65 / 58J45
Key words: Finite volume method / conservation law / curved manifold
© EDP Sciences, SMAI, 2009
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