# A convergence result for finite volume schemes on Riemannian manifolds

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

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

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topGiesselmann, 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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