Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes

Date

2009-07-01

Author

Lefloch, Philippe G.
Okutmuştur, Baver
Neves, Wladimir

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Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L (1)-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 L (1) 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 extend the arguments to curved manifolds, by taking into account the effects to the geometry and overcoming several new technical difficulties.

Subject Keywords

Applied Mathematics, General Mathematics

URI

https://hdl.handle.net/11511/40640

Journal

ACTA MATHEMATICA SINICA-ENGLISH SERIES

DOI

https://doi.org/10.1007/s10114-009-8090-y

Collections

Department of Mathematics, Article

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Citation Formats

P. G. Lefloch, B. Okutmuştur, and W. Neves, “Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes,” ACTA MATHEMATICA SINICA-ENGLISH SERIES, pp. 1041–1066, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/40640.