A CONVERGENCE RESULT FOR FINITE VOLUME SCHEMES ON RIEMANNIAN MANIFOLDS

摘要

This paper studies a family of finite volume schemes for the hyperbolic scalar conservation law ut + V_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~4/1 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~2/1 .