The multigrid method applied to a finite-element scheme for a two-dimensional Stokes-type system
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 12, pp. 1797-1803
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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.
@article{ZVMMF_1990_30_12_a4,
author = {B. V. Pal'tsev and I. I. Chechel'},
title = {The multigrid method applied to a~finite-element scheme for a~two-dimensional {Stokes-type} system},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1797--1803},
publisher = {mathdoc},
volume = {30},
number = {12},
year = {1990},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_12_a4/}
}
TY - JOUR AU - B. V. Pal'tsev AU - I. I. Chechel' TI - The multigrid method applied to a finite-element scheme for a two-dimensional Stokes-type system JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 1990 SP - 1797 EP - 1803 VL - 30 IS - 12 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_12_a4/ LA - ru ID - ZVMMF_1990_30_12_a4 ER -
%0 Journal Article %A B. V. Pal'tsev %A I. I. Chechel' %T The multigrid method applied to a finite-element scheme for a two-dimensional Stokes-type system %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 1990 %P 1797-1803 %V 30 %N 12 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_12_a4/ %G ru %F ZVMMF_1990_30_12_a4
B. V. Pal'tsev; I. I. Chechel'. The multigrid method applied to a finite-element scheme for a two-dimensional Stokes-type system. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 12, pp. 1797-1803. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_12_a4/