A convergence result for finite volume schemes on riemannian manifolds
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 5, pp. 929-955.
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This paper studies a family of finite volume schemes for the hyperbolic scalar conservation law on a closed riemannian manifold For an initial value in BV() we will show that these schemes converge with a convergence rate towards the entropy solution. When is -dimensional the schemes are TVD and we will show that this improves the convergence rate to
DOI :
10.1051/m2an/2009013
Classification :
74S10, 35L65, 58J45
Mots-clés : finite volume method, conservation law, curved manifold
Mots-clés : finite volume method, conservation law, curved manifold
@article{M2AN_2009__43_5_929_0, author = {Giesselmann, Jan}, title = {A convergence result for finite volume schemes on riemannian manifolds}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {929--955}, publisher = {EDP-Sciences}, volume = {43}, number = {5}, year = {2009}, doi = {10.1051/m2an/2009013}, zbl = {1173.74454}, mrnumber = {2559739}, language = {en}, url = {https://geodesic-test.mathdoc.fr/articles/10.1051/m2an/2009013/} }
TY - JOUR AU - Giesselmann, Jan TI - A convergence result for finite volume schemes on riemannian manifolds JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2009 SP - 929 EP - 955 VL - 43 IS - 5 PB - EDP-Sciences UR - https://geodesic-test.mathdoc.fr/articles/10.1051/m2an/2009013/ DO - 10.1051/m2an/2009013 LA - en ID - M2AN_2009__43_5_929_0 ER -
%0 Journal Article %A Giesselmann, Jan %T A convergence result for finite volume schemes on riemannian manifolds %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2009 %P 929-955 %V 43 %N 5 %I EDP-Sciences %U https://geodesic-test.mathdoc.fr/articles/10.1051/m2an/2009013/ %R 10.1051/m2an/2009013 %G en %F M2AN_2009__43_5_929_0
Giesselmann, Jan. A convergence result for finite volume schemes on riemannian manifolds. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 5, pp. 929-955. doi : 10.1051/m2an/2009013. https://geodesic-test.mathdoc.fr/articles/10.1051/m2an/2009013/
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