Geodesic
About one choice of essentially non-oscillatory high occuracy order difference scheme for systems of conservation laws
Matematičeskoe modelirovanie, Tome 21 (2009) no. 11, pp. 19-32

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Version of essentially non-oscillatory high occuracy order difference scheme for systems of conservation laws, based on minimization for norm of interpolation polynomial deviation from the cell averages was suggested in this paper. Such choice can give more monotonous solution in comparision with traditional ENO and WENO schemes of corresponding occuracy order, that was confirmed by results of numerical calculation for model problems. 
@article{MM_2009_21_11_a2,
     author = {M. E. Ladonkina and O. A. Neklyudova and V. F. Tishkin and V. S. Chevanin},
     title = {About one choice of essentially non-oscillatory high occuracy order difference scheme for systems of conservation laws},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {19--32},
     publisher = {mathdoc},
     volume = {21},
     number = {11},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2009_21_11_a2/}
}
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M. E. Ladonkina; O. A. Neklyudova; V. F. Tishkin; V. S. Chevanin. About one choice of essentially non-oscillatory high occuracy order difference scheme for systems of conservation laws. Matematičeskoe modelirovanie, Tome 21 (2009) no. 11, pp. 19-32. http://geodesic.mathdoc.fr/item/MM_2009_21_11_a2/