Geodesic
On convergence rate of WENO schemes behind a shock front
Matematičeskoe modelirovanie, Tome 27 (2015) no. 2, pp. 129-138

Voir la notice de l'article provenant de la source Math-Net.Ru

The numerical analysis has shown that high order finite-volume WENO schemes have only the first order of convergence in the smooth part of weak solution behind a shock front. The order of integral convergence of difference solution is found to estimate accuracy of translation of Rankine–Hugoniot conditions through the shock.
Keywords: finite-volume WENO schemes, Rankine–Hugoniot conditions, integral convergence, order of convergence. 
@article{MM_2015_27_2_a8,
     author = {N. A. Mikhailov},
     title = {On convergence rate of {WENO} schemes behind a shock front},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {129--138},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2015_27_2_a8/}
}
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N. A. Mikhailov. On convergence rate of WENO schemes behind a shock front. Matematičeskoe modelirovanie, Tome 27 (2015) no. 2, pp. 129-138. http://geodesic.mathdoc.fr/item/MM_2015_27_2_a8/