Geodesic
Uniform algorithm for computation of discontinuous solution on adaptive grids
Matematičeskoe modelirovanie, Tome 6 (1994) no. 11, pp. 25-40 Cet article a éte moissonné depuis la source Math-Net.Ru

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The numerical method for computation of model transfer equation ${\partial u}/{\partial t}+{\partial u}/{\partial x}=0$ on solution-adaptive grids is presented. The adaptation of grid is based on method of equidistribution weight function. The corresponding choice of weight function and the use of high order monotonous scheme allows to receive second accuracy order both for discontinuous and for smooth solutions. 
@article{MM_1994_6_11_a2,
     author = {V. I. Pokhilko and V. F. Tishkin},
     title = {Uniform algorithm for computation of discontinuous solution on adaptive grids},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {25--40},
     year = {1994},
     volume = {6},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1994_6_11_a2/}
}
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V. I. Pokhilko; V. F. Tishkin. Uniform algorithm for computation of discontinuous solution on adaptive grids. Matematičeskoe modelirovanie, Tome 6 (1994) no. 11, pp. 25-40. http://geodesic.mathdoc.fr/item/MM_1994_6_11_a2/