| Issue |
ESAIM: M2AN
Volume 43, Number 5, September-October 2009
|
|
|---|---|---|
| Page(s) | 929 - 955 | |
| DOI | https://doi.org/10.1051/m2an/2009013 | |
| Published online | 12 June 2009 | |
A convergence result for finite volume schemes on Riemannian manifolds
Universität Stuttgart (IANS), Pfaffenwaldring 57, 70569 Stuttgart, Germany. jan.giesselmann@mathematik.uni-stuttgart.de
Received:
30
July
2008
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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