Hyperbolic conservation laws on manifolds. Error estimate for finite volume schemes

Details Hyperbolic conservation laws on manifolds. Error estimate for finite volume schemes Hyperbolic conservation laws on manifolds. Error estimate for finite volume schemes

2008-07-29

arxiv.org/abs/0807.4640v1

Mathematics

Analysis of PDEs

32 pages

Scientific paper

Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L1-error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L1 norm is of order h^(1/4) at most, where h represents the maximal diameter of elements in the family 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 extent the arguments to curved manifolds, by taking into account the effects to the geometry and overcoming several new technical difficulties.

Affiliated with

Also associated with

No associations

Rating

Hyperbolic conservation laws on manifolds. Error estimate for finite volume schemes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hyperbolic conservation laws on manifolds. Error estimate for finite volume schemes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hyperbolic conservation laws on manifolds. Error estimate for finite volume schemes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-38674