A convergence result for finite volume schemes on Riemannian manifolds

Jan Giesselmann

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

  • Volume: 43, Issue: 5, page 929-955
  • ISSN: 0764-583X

Abstract

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This paper studies a family of finite volume schemes for the hyperbolic scalar conservation law u t + g · f ( x , u ) = 0 on a closed Riemannian manifold M. For an initial value in BV(M) we will show that these schemes converge with a h 1 4 convergence rate towards the entropy solution. When M is 1-dimensional the schemes are TVD and we will show that this improves the convergence rate to h 1 2 .

How to cite

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Giesselmann, Jan. "A convergence result for finite volume schemes on Riemannian manifolds." ESAIM: Mathematical Modelling and Numerical Analysis 43.5 (2009): 929-955. <http://eudml.org/doc/250606>.

@article{Giesselmann2009,
abstract = { This paper studies a family of finite volume schemes for the hyperbolic scalar conservation law $u_t +\nabla_g \cdot f(x,u)=0$ on a closed Riemannian manifold M. For an initial value in BV(M) we will show that these schemes converge with a $h^\{\frac\{1\}\{4\}\} $ convergence rate towards the entropy solution. When M is 1-dimensional the schemes are TVD and we will show that this improves the convergence rate to $h^\{\frac\{1\}\{2\}\}.$},
author = {Giesselmann, Jan},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Finite volume method; conservation law; curved manifold; finite volume method},
language = {eng},
month = {6},
number = {5},
pages = {929-955},
publisher = {EDP Sciences},
title = {A convergence result for finite volume schemes on Riemannian manifolds},
url = {http://eudml.org/doc/250606},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Giesselmann, Jan
TI - A convergence result for finite volume schemes on Riemannian manifolds
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2009/6//
PB - EDP Sciences
VL - 43
IS - 5
SP - 929
EP - 955
AB - This paper studies a family of finite volume schemes for the hyperbolic scalar conservation law $u_t +\nabla_g \cdot f(x,u)=0$ on a closed Riemannian manifold M. For an initial value in BV(M) we will show that these schemes converge with a $h^{\frac{1}{4}} $ convergence rate towards the entropy solution. When M is 1-dimensional the schemes are TVD and we will show that this improves the convergence rate to $h^{\frac{1}{2}}.$
LA - eng
KW - Finite volume method; conservation law; curved manifold; finite volume method
UR - http://eudml.org/doc/250606
ER -

References

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