The method of total approximation for singularly perturbed elliptic equations with convective terms
Matematičeskoe modelirovanie, Tome 13 (2001) no. 4, pp. 95-108.

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The Dirichlet problem for elliptic equations is considered on an $n$-dimensional parallelepiped. The highest derivatives of the equation are multiplied by a parameter $\varepsilon$ taking arbitrary values from the half-interval (0,1]. When $\varepsilon=0$, the elliptic equations degenerate into first-order ones which contain derivatives with respect to the space variables, i.e. convective terms. To solve the boundary value problem, we construct a finite difference scheme that converges $\varepsilon$-uniformly. The construction of this scheme is done on the basis of the method of total approximation; $\varepsilon$-uniform convergence of the difference scheme is achieved due to the use of special piecewise uniform meshes condensing in the neighbourhood of boundary layers.
@article{MM_2001_13_4_a7,
     author = {G. I. Shishkin},
     title = {The method of total approximation for singularly perturbed elliptic equations with convective terms},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {95--108},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2001_13_4_a7/}
}
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G. I. Shishkin. The method of total approximation for singularly perturbed elliptic equations with convective terms. Matematičeskoe modelirovanie, Tome 13 (2001) no. 4, pp. 95-108. http://geodesic.mathdoc.fr/item/MM_2001_13_4_a7/