A Convergence Result for Finite Volume Schemes on 2 -dimensional Riemannian Manifolds
نویسنده
چکیده
This paper studies a family of nite volume schemes for the hyperbolic scalar conservation law ut +∇g · f(x, u) = 0 on a closed Riemannian manifold. For an initial value in BV(M) and an at most 2 -dimensional manifold 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 .
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تاریخ انتشار 2008