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A convergence result for finite volume schemes on Riemannian manifolds

Published online by Cambridge University Press:  12 June 2009

Jan Giesselmann*
Universität Stuttgart (IANS), Pfaffenwaldring 57, 70569 Stuttgart, Germany.
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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 $h^{\frac{1}{2}}.$

Research Article
© EDP Sciences, SMAI, 2009

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