Geodesic
Convenient system of FEM test functions for computational fluid dynamics
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1961-1972 
S. E. Zakiev; L. P. Kholpanov. Convenient system of FEM test functions for computational fluid dynamics. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1961-1972. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a9/
@article{ZVMMF_2010_50_11_a9,
     author = {S. E. Zakiev and L. P. Kholpanov},
     title = {Convenient system of {FEM} test functions for computational fluid dynamics},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1961--1972},
     year = {2010},
     volume = {50},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a9/}
}
TY  - JOUR
AU  - S. E. Zakiev
AU  - L. P. Kholpanov
TI  - Convenient system of FEM test functions for computational fluid dynamics
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 1961
EP  - 1972
VL  - 50
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a9/
LA  - ru
ID  - ZVMMF_2010_50_11_a9
ER  - 
%0 Journal Article
%A S. E. Zakiev
%A L. P. Kholpanov
%T Convenient system of FEM test functions for computational fluid dynamics
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 1961-1972
%V 50
%N 11
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a9/
%G ru
%F ZVMMF_2010_50_11_a9

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

For the development of finite element schemes, a fundamentally new system of test functions defined on a finite element that is a convex quadrilateral is proposed. Due to the remarkable properties of the system (specifically, mutual orthogonality), the resulting matrices can be simplified and the corresponding construction procedures can be made more transparent, especially for problems in computational fluid dynamics. Thus, the system of test functions may play an important role in finite element methods as applied to two-dimensional problems.

[1] Marchuk G. I., Agoshkov V. I., Vvedenie v proektsionno-setochnye metody, Nauka, M., 1981 | MR

[2] Streng G., Fiks Dzh., Teoriya metoda konechnykh elementov, Mir, M., 1977 | MR

[3] Fletcher K., Chislennye metody na osnove metoda Galerkina, Mir, M., 1988

[4] Zienkievich O. C., Taylor R. L., The finite element methods, v. I–III, Butterworth-Heinemann, 2000

[5] Chung T. G., Computational fluid dynamics, Cambridge Univ. Press, 2002 | MR

[6] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1981 | MR

[7] Zienkiewcz O. C., The finite element method in engineering science, McGrow-Hill, New York, 1971 | MR