Geodesic
Preconditioner for a Laplace grid operator on a condensed grid
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 2, pp. 165-170 
A. M. Matsokin. Preconditioner for a Laplace grid operator on a condensed grid. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 2, pp. 165-170. http://geodesic.mathdoc.fr/item/SJVM_2013_16_2_a5/
@article{SJVM_2013_16_2_a5,
     author = {A. M. Matsokin},
     title = {Preconditioner for {a~Laplace} grid operator on a~condensed grid},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {165--170},
     year = {2013},
     volume = {16},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2013_16_2_a5/}
}
TY  - JOUR
AU  - A. M. Matsokin
TI  - Preconditioner for a Laplace grid operator on a condensed grid
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2013
SP  - 165
EP  - 170
VL  - 16
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SJVM_2013_16_2_a5/
LA  - ru
ID  - SJVM_2013_16_2_a5
ER  - 
%0 Journal Article
%A A. M. Matsokin
%T Preconditioner for a Laplace grid operator on a condensed grid
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2013
%P 165-170
%V 16
%N 2
%U http://geodesic.mathdoc.fr/item/SJVM_2013_16_2_a5/
%G ru
%F SJVM_2013_16_2_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, it is proved that a Laplace grid operator approximating a Dirichlet boundary value problem for the Poisson equation by the finite element method with piecewise-linear functions on an evenly condensed grid that is topologically equivalent to a rectangular grid (i.e. obtained by shifting the rectangular grid nodes) is equivalent, in the range, to the operator of a $5$-point difference scheme on a uniform grid.

[1] Matsokin A. M., Variatsionno-raznostnyi metod resheniya ellipticheskikh uravnenii v kruge, Preprint No 13, AN SSSR. Sib. otd-nie. VTs, Novosibirsk, 1975

[2] Kuznetsov Yu. A., “Vychislitelnye metody v podprostranstvakh”, Vychislitelnye protsessy i sistemy, 2, Nauka, M., 1985, 264–350

[3] Oganesyan L. A., Rivkind V. Ya., Rukhovets L. A., Variatsionno-raznostnye metody resheniya ellipticheskikh uravnenii, Ch. I, Differentsialnye uravneniya i ikh prilozheniya, 5, Pyargale, Vilnyus, 1973; Вариационно-разностные методы решения эллиптических уравнений, Ч. II, Дифференциальные уравнения и их приложения, 8, Пяргале, Вильнюс, 1974

[4] Oganesyan L. A., Rukhovets L. A., Variatsionno-raznostnye metody resheniya ellipticheskikh uravnenii, Izd-vo AN ArmSSR, Erevan, 1979

[5] Dyakonov E. G., Minimizatsiya vychislitelnoi raboty: Asimptoticheski optimalnye algoritmy dlya ellipticheskikh zadach, Nauka, M., 1989 | MR