Geodesic
On rapidly converging iterative methods with incomplete splitting of boundary conditions for a~multidimensional singularly perturbed system of Stokes type
Sbornik. Mathematics, Tome 81 (1995) no. 2, pp. 487-531

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Constructed and investigated are iterative methods for solving the Dirichlet problem for a system with small parameter $\varepsilon >0$: $$ -\varepsilon^2\Delta\mathbf{u}+\mathbf{u}+\operatorname{grad}p=\mathbf{f},\qquad \operatorname{div}\mathbf{u}=0, $$ leading at each iteration to splitting into a Neumann problem for the pressure and a vector Dirichlet–Neumann problem for the velocities. The case of periodic 'flows' between parallel walls is studied. The fastest variants of the method have the rate of convergence of a geometric progression with ratio of order $\varepsilon$. Also obtained are '$\varepsilon$-coercive' estimates of the solutions of the original problem in Sobolev norms. 
@article{SM_1995_81_2_a10,
     author = {B. V. Pal'tsev},
     title = {On rapidly converging iterative methods with incomplete splitting of boundary conditions for a~multidimensional singularly perturbed system of {Stokes} type},
     journal = {Sbornik. Mathematics},
     pages = {487--531},
     publisher = {mathdoc},
     volume = {81},
     number = {2},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_81_2_a10/}
}
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B. V. Pal'tsev. On rapidly converging iterative methods with incomplete splitting of boundary conditions for a~multidimensional singularly perturbed system of Stokes type. Sbornik. Mathematics, Tome 81 (1995) no. 2, pp. 487-531. http://geodesic.mathdoc.fr/item/SM_1995_81_2_a10/