This article is cited in 1 paper

The multigrid method applied to a finite-element scheme for a two-dimensional Stokes-type system

B. V. Pal'tsev, I. I. Chechel'

Moscow

Abstract: A two-dimensional system of the Stokes type, in which the coefficient of the highest order derivatives is a small parameter $\varepsilon>0$, is considered, and a version of the multigrid method is developed to handle a finite-element scheme for the system, obtained by using biquadratic elements for the velocities, linear elements for the pressure and an approximatively-solenoidal basis. Approximatively-solenoidal interpolations are defined and used to design the coarse-grid bases. Numerical experiments demonstrate a high rate of convergence even for very small $\varepsilon$ values.

UDC: 519.6:532.5

MSC: Primary 76M10; Secondary 76D07, 65N55

Received: 24.04.1990

 English version: USSR Computational Mathematics and Mathematical Physics, 1990, 30:6, 141–146

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