Finite volume schemes on Lorentzian manifolds

Date

2008

Author

Amorim, P.
LeFloch, P. G.
Okutmuştur, Baver

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 United States License.

Item Usage Stats

257
views

0
downloads

We investigate the numerical approximation of (discontinuous) entropy solutions to nonlinear hyperbolic conservation laws posed on a Lorentzian manifold. Our main result establishes the convergence of monotone and first-order finite volume schemes for a large class of (space and time) triangulations. The proof relies on a discrete version of entropy inequalities and an entropy dissipation bound, which take into account the manifold geometry and were originally discovered by Cockburn, Coquel, and LeFloch in the (flat) Euclidian setting.

Subject Keywords

Conservation law, Lorenzian manifold, Entropy condition, Measure-valued solution, finite volume scheme, Convergence analysis

URI

https://hdl.handle.net/11511/28627

Journal

Communications in Mathematical Sciences

DOI

https://doi.org/10.4310/cms.2008.v6.n4.a13

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes Lefloch, Philippe G.; Okutmuştur, Baver; Neves, Wladimir (Springer Science and Business Media LLC, 2009-07-01) 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 theo...
Energetics and stability of discrete charge distribution on the surface of a sphere Oymak, H; Erkoç, Şakir (World Scientific Pub Co Pte Lt, 2001-02-01) We have investigated the minimum-energy distribution of N, 3 ≤ N ≤ 97, equal point charges confined to the surface of a sphere. Charges interact with each other via the Coulomb potential of the form 1/r. Minimum-energy distributions have been determined by minimizing the tangential forces on each charge. Further numerical evidence shows that in the minimum-energy state of N charges on the sphere, it is not possible to place a charge at the geometrical center. Besides, it has been found that the most and rel...
Chaotic period-doubling and OGY control for the forced Duffing equation Akhmet, Marat (2012-04-01) In this paper we consider the Duffing equation forced with a pulse function, whose moments of discontinuity depend on the initial data. Existence of the chaos through period-doubling cascade is proved, and the OGY control method is used to stabilize the periodic solutions. Appropriate simulations of the chaos and stabilized periodic solutions are presented.
An answer to a question of Cao, Reilly and Xiong Ercan, Z.; Onal, S. (Institute of Mathematics, Czech Academy of Sciences, 2006-01-01) We present a simple proof of a Banach-Stone type Theorem. The method used in the proof also provides an answer to a conjecture of Cao, Reilly and Xiong.
The exponential of a constant matrix on time scales Zafer, Ağacık (Cambridge University Press (CUP), 2006-07-01) In this paper we describe an elementary method for calculating the matrix exponential on an arbitrary time scale. An example is also given to illustrate the result.

Citation Formats

P. Amorim, P. G. LeFloch, and B. Okutmuştur, “Finite volume schemes on Lorentzian manifolds,” Communications in Mathematical Sciences, pp. 1059–1086, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/28627.