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This article is cited in 30 scientific papers (total in 30 papers)
On rapidly converging iterative methods with incomplete splitting of boundary conditions for a multidimensional singularly perturbed system of Stokes type
B. V. Pal'tsev Dorodnitsyn Computing Centre of the Russian Academy of Sciences
Abstract:
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.
Received: 20.07.1993
Citation:
B. V. Pal'tsev, “On rapidly converging iterative methods with incomplete splitting of boundary conditions for a multidimensional singularly perturbed system of Stokes type”, Mat. Sb., 185:4 (1994), 101–150; Russian Acad. Sci. Sb. Math., 81:2 (1995), 487–531
Linking options:
https://www.mathnet.ru/eng/sm893https://doi.org/10.1070/SM1995v081n02ABEH003548 https://www.mathnet.ru/eng/sm/v185/i4/p101
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Abstract page: | 304 | Russian version PDF: | 139 | English version PDF: | 7 | References: | 39 | First page: | 2 |
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