Geodesic
A semi-Lagrangian method on dynamically adapted grid for two-dimensional advection problem
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1219-1228

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We develop a semi-Lagrangian algorithm for solving the two-dimensional advection problem. A numerical solution is constructed as a piecewise constant function on neighborhood of grid node. The proposed method is stable and gives an approximate solution with the first order of accuracy for smooth solutions. We use dynamically adaptive grid. As initial guest we consider rectangular grid.
Keywords: semi-Lagrangian method, adaptive grid
Mots-clés : advection problem. 
@article{SEMR_2016_13_a99,
     author = {A. V. Vyatkin and E. V. Kuchunova and V. V. Shaydurov},
     title = {A {semi-Lagrangian} method on dynamically adapted grid for two-dimensional advection problem},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1219--1228},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a99/}
}
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A. V. Vyatkin; E. V. Kuchunova; V. V. Shaydurov. A semi-Lagrangian method on dynamically adapted grid for two-dimensional advection problem. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1219-1228. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a99/