Geodesic
On one approach to constructing schemes of increased order of accuracy in the finite element method
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 4, pp. 287-300 
A. A. Bubyakin; Yu. M. Laevsky. On one approach to constructing schemes of increased order of accuracy in the finite element method. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 4, pp. 287-300. http://geodesic.mathdoc.fr/item/SJVM_2004_7_4_a1/
@article{SJVM_2004_7_4_a1,
     author = {A. A. Bubyakin and Yu. M. Laevsky},
     title = {On one approach to constructing schemes of increased order of accuracy in the finite element method},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {287--300},
     year = {2004},
     volume = {7},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2004_7_4_a1/}
}
TY  - JOUR
AU  - A. A. Bubyakin
AU  - Yu. M. Laevsky
TI  - On one approach to constructing schemes of increased order of accuracy in the finite element method
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2004
SP  - 287
EP  - 300
VL  - 7
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SJVM_2004_7_4_a1/
LA  - ru
ID  - SJVM_2004_7_4_a1
ER  - 
%0 Journal Article
%A A. A. Bubyakin
%A Yu. M. Laevsky
%T On one approach to constructing schemes of increased order of accuracy in the finite element method
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2004
%P 287-300
%V 7
%N 4
%U http://geodesic.mathdoc.fr/item/SJVM_2004_7_4_a1/
%G ru
%F SJVM_2004_7_4_a1

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

The paper considers schemes of increased order of accuracy in the finite element method with the same number of degrees of freedom as in the schemes constructed by the Galerkin method with the use of piecewisepolynomial functions. The approach proposed is based on a special choice of the grid scalar products and the right-hand side linear functionals limited on a set of grid functions. The fourth order of accuracy is established in the grid energy norm.

[1] Mikeladze Sh. B., “O chislennom integrirovanii uravnenii Laplasa i Puassona”, Dokl. AN SSSR, 14:4 (1937), 181–182

[2] Samarskii A. A., Vvedenie v teoriyu raznostnykh skhem, Nauka, M., 1971 | MR | Zbl

[3] Ilin V. P., Metody konechnykh raznostei i konechnykh ob'emov dlya ellipticheskikh uravnenii, Izd-vo IM SO RAN, Novosibirsk, 2000

[4] Lebedev V. I., Tsapelkin E. S., “O vliyanii vybora koordinatnykh funktsii na strukturu uravnenii metoda Galerkina”, Sb. Variatsionno-raznostnye metody v matematicheskoi fizike, Izd-vo VTs SO A N SSSR, Novosibirsk, 1974, 47–58 | MR

[5] Strelkov N. A., “O lokalnoi approksimatsii proektsionno-raznostnykh metodov”, Zhurn. vychisl. matem. i mat. fiziki, 34:2 (1994), 201–213 | MR | Zbl

[6] Il'in V. P., Laevsky Yu. M., “On the compact schemes of high order accuracy in finite element method”, Rus. J. of Numer. Anal. and Math. Modell., 17:1 (2002), 25–39 | MR

[7] Syarle F., Metod konechnykh elementov dlya ellipticheskikh zadach, Mir, M., 1980 | MR

[8] Bubyakin A. A., Laevskii Yu. M., “Ob odnoi variatsionno-raznostnoi skheme povyshennogo poryadka tochnosti resheniya trekhmernogo uravneniya Puassona”, Vestnik NGU, 2:2 (2002), 19–31 | Zbl

[9] Oganesyan L. A., Rukhovets L. A., Variatsionno-raznostnye metody resheniya ellipticheskikh uravnenii, Izd-vo AN Arm. SSR, Erevan, 1979 | MR

[10] Samarskii A. A., Andreev V. B., Raznostnye metody dlya ellipticheskikh uravnenii, Nauka, M., 1976 | MR | Zbl