On rapidly convergent iterative methods with complete boundary-condition splitting for a multidimensional singularly perturbed system of Stokes type

B. V. Pal'tsev

Sbornik. Mathematics, Tome 83 (1995) no. 1, pp. 93-118

Résumé

This paper is an investigation of a group of iterative methods with complete boundary-condition splitting for solving the first boundary value problem for a system of Stokes type with a small parameter $\varepsilon>0$: \begin{gather*} -\varepsilon ^2\Delta{\mathbf u}+{\mathbf u}+\operatorname{grad}p={\mathbf f}, \qquad \operatorname{div}{\mathbf u}=0\quad \text {in </nomathmode><mathmode>$\Omega $}, {\mathbf u}|_\Gamma ={\mathbf g}, \qquad \int _\Gamma ({\mathbf g},{\mathbf n}) ds=0, \end{gather*}</mathmode><nomathmode> where $\mathbf{u}=(u^1(x),\dots,u^n(x))$ is the velocity vector, $p = p(x)$ is the pressure, $\mathbf{f}=(f^1(x),\dots,f^n(x))$ is the field of external forces, and $\mathbf{g}=(g^1(x),\dots,g^n(x))$ is a given value of the velocity vector on the boundary $\Gamma$ of a domain $\Omega$ in the $n$-dimensional Euclidean space $\mathbb{R}^n$.

Bibliographie

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