Geodesic
An error estimate for a numerical scheme for the compressible Navier-stokes system
Kragujevac Journal of Mathematics, Tome 30 (2007) no. 1

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The subject of this paper is an error estimate of the order $h^{1/2}$ in the $L^2$-norm for an explicit, fully discrete numerical scheme that approximates smooth solutions of the barotropic compressible fluid flow equations in the multidimensional case. Assuming some a-priori estimates for the discrete solution we derive an error estimate using a technique based upon stability results due to Dafermos \cite{Da} and DiPerna \cite{Di}, which were originally formulated for systems of conservation laws. 
@article{KJM_2007_30_1_a19,
     author = {Vladimir Jovanovi\'c},
     title = {An error estimate for a numerical scheme for the compressible {Navier-stokes} system},
     journal = {Kragujevac Journal of Mathematics},
     pages = {263 - 275},
     publisher = {mathdoc},
     volume = {30},
     number = {1},
     year = {2007},
     zbl = {1195.76151},
     url = {http://geodesic.mathdoc.fr/item/KJM_2007_30_1_a19/}
}
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Vladimir Jovanović. An error estimate for a numerical scheme for the compressible Navier-stokes system. Kragujevac Journal of Mathematics, Tome 30 (2007) no. 1. http://geodesic.mathdoc.fr/item/KJM_2007_30_1_a19/