Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes
Date
2009-07-01
Author
Lefloch, Philippe G.
Okutmuştur, Baver
Neves, Wladimir
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
310
views
0
downloads
Cite This
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
Suggestions
OpenMETU
Core
Hyperbolic conservation laws on manifolds with limited regularity
Lefloch, Philippe G.; Okutmuştur, Baver (Elsevier BV, 2008-05-01)
We introduce a formulation of the initial and boundary value problem for nonlinear hyperbolic conservation laws posed on a differential manifold endowed with a volume form, possibly with a boundary; in particular, this includes the important case of Lorentzian manifolds. Only limited regularity is assumed on the geometry of the manifold. For this problem, we establish the existence and uniqueness of an L-1 semi-group of weak solutions satisfying suitable entropy and boundary conditions.
Exact quantization rule to the Kratzer-type potentials: an application to the diatomic molecules
IKHDAİR, SAMEER; Sever, Ramazan (Springer Science and Business Media LLC, 2009-04-01)
For arbitrary values of n and l quantum numbers, we present a simple exact analytical solution of the D-dimensional (D a parts per thousand yen 2) hyperradial Schrodinger equation with the Kratzer and the modified Kratzer potentials within the framework of the exact quantization rule (EQR) method. The exact bound state energy eigenvalues (E (nl) ) are easily calculated from this EQR method. The corresponding normalized hyperradial wave functions (psi (nl) (r)) are also calculated. The exact energy eigenvalu...
Asymptotic behavior of solutions of differential equations with piecewise constant arguments
Akhmet, Marat (Elsevier BV, 2008-09-01)
The main goal of the work is to obtain sufficient conditions for the asymptotic equivalence of a linear system of ordinary differential equations and a quasilinear system of differential equations with piecewise constant argument.
Dynamic programming for a Markov-switching jump-diffusion
Azevedo, N.; Pinheiro, D.; Weber, Gerhard Wilhelm (Elsevier BV, 2014-09-01)
We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump-diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman's optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton-Jacobi-Belman equation, which turns out to be a partial in...
Global existence and boundedness for a class of second-order nonlinear differential equations
Tiryaki, Aydin; Zafer, Ağacık (Elsevier BV, 2013-09-01)
In this paper we obtain new conditions for the global existence and boundedness of solutions for nonlinear second-order equations of the form
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
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.