A CONVERGENCE RESULT FOR FINITE VOLUME SCHEMES ON RIEMANNIAN MANIFOLDS

This paper studies a family of finite volume schemes for the hyperbolic scalar conservation law u(t) + del(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.