Geodesic
Grid approximation of boundary value problems for singularly perturbed quasi-linear elliptic equations with interior layer
Matematičeskoe modelirovanie, Tome 7 (1995) no. 2, pp. 72-88 
G. I. Shishkin. Grid approximation of boundary value problems for singularly perturbed quasi-linear elliptic equations with interior layer. Matematičeskoe modelirovanie, Tome 7 (1995) no. 2, pp. 72-88. http://geodesic.mathdoc.fr/item/MM_1995_7_2_a5/
@article{MM_1995_7_2_a5,
     author = {G. I. Shishkin},
     title = {Grid approximation of boundary value problems for singularly perturbed quasi-linear elliptic equations with interior layer},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {72--88},
     year = {1995},
     volume = {7},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1995_7_2_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The first boundary value problem for two dimension quasi-linear elliptic equation of second order is considered. Highest derivatives of the equation are multiplied by a parameter which can get any value on interval $(0,1]$. When the parameter is equal to zero the reduced equation is a quasi-linear first order equation. An interior layer appears when the parameter tends to zero. The considered problem is as model for problems which appear when the non-linear shock waves are investigated. With using of special condensing grids we construct the special difference schemes, which converge uniformly with respect the parameter.