Philippe G.LeFLOCH, Baver OKUTMUSTUR, Wladimir NEVES
Following Ben–Artzi and LeFloch,we consider nonlinear hyperbolic conservation lawsposed on a Riemannian manifold,and we establish an L1-error estimate for a class of finite volumeschemes allowing for the approximation of entropy solutions to the initial value problem.The errorin the L1 norm is of order h1/4 at most,where h represents the maximal diameter of elements in thefamily of geodesic triangulations.The proof relies on a suitable generalization of Cockburn,Coquel,and LeFloch's theory which was originally developed in the Euclidian setting.We extend the argumentsto curved manifolds,by taking into account the e?ects to the geometry and overcoming several newtechnical diffculties.