Spectral element method for boundary value problems on unstructered grid
Matematičeskoe modelirovanie, Tome 19 (2007) no. 10, pp. 3-14.

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

The computation technology in constructing two dimensional boundary value problems by means of spectral element method is described in this paper. The given method allows to find solution of high accuracy on coarse unstructed grids. The solutions obtained with this method serve for local approximation algorithms testing and also may have independent meaning in development devices and systems of high accuracy.
@article{MM_2007_19_10_a0,
     author = {A. M. Bubenchikov and V. S. Poponin and D. K. Firsov},
     title = {Spectral element method for boundary value problems on unstructered grid},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--14},
     publisher = {mathdoc},
     volume = {19},
     number = {10},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2007_19_10_a0/}
}
TY  - JOUR
AU  - A. M. Bubenchikov
AU  - V. S. Poponin
AU  - D. K. Firsov
TI  - Spectral element method for boundary value problems on unstructered grid
JO  - Matematičeskoe modelirovanie
PY  - 2007
SP  - 3
EP  - 14
VL  - 19
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2007_19_10_a0/
LA  - ru
ID  - MM_2007_19_10_a0
ER  - 
%0 Journal Article
%A A. M. Bubenchikov
%A V. S. Poponin
%A D. K. Firsov
%T Spectral element method for boundary value problems on unstructered grid
%J Matematičeskoe modelirovanie
%D 2007
%P 3-14
%V 19
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2007_19_10_a0/
%G ru
%F MM_2007_19_10_a0
A. M. Bubenchikov; V. S. Poponin; D. K. Firsov. Spectral element method for boundary value problems on unstructered grid. Matematičeskoe modelirovanie, Tome 19 (2007) no. 10, pp. 3-14. http://geodesic.mathdoc.fr/item/MM_2007_19_10_a0/

[1] Fletcher K., Vychislitelnye metody v dinamike zhidkostei, Mir, M., 1991

[2] Zienkiewicz O. C., The finite Element Method: Fluid Dynamics, Oxford, 2000

[3] Bailey F. R., Numerical Aerodynamic Simulation Program, Overview of NASA's

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

[5] Boyd J. P., Chebyshev and Fourier Spectral Methods, Second Edition, University of Michigan, 2000 | MR | Zbl

[6] Van de Vosse F. N., Spectral Element Methods: theory and application, Oxford University Press, London, 1999

[7] Fournier Aime, “Spectral Element Method. Part 1: Numerical Algorithm”, Annual Conf. CMD, Canada, 2000, 6/11–3

[8] Andersen J. D., Computational Fluid Dynamics, New York, 1996

[9] Saad Y., Iterative Methods for Sparse Linear Systems, 2000

[10] Ilin V. P., Metody nepolnoi faktorizatsii dlya resheniya algebraicheskikh sistem, Nauka, M., 1995 | MR

[11] Ilin V. P., Chislennyi analiz, Chast 1, Novosibirsk, 2004

[12] Tolstykh A. I., Kompaktnye raznostnye skhemy i ikh primeneniya v zadachakh aerogidrodinamiki, M., 1986

[13] Helenbrook B. T., A Two-Fluid Spectral Element Method, Department of Mechanical and aeronautical engineering, 1999

[14] Pasquetti R., Spectral Element Methods on triangles and quadliterals: comparisons and applications, Universite de Nice, 2001

[15] Heinrich W., “Spectral shemes on triangular elements”, J. Comp. Physics, 1998

[16] Lee I., An $O(n\ln n)$ solution algorithm for spectral element methods, MIT, 2003

[17] Press W. H., Vetterling W. T., Numerical Receipes in $C^{++}$, Cambridge University Press, 2002 | MR

[18] Roth M. J., Nodal Configurations and Voronoi Tessellations for Triangular Spectral Elements, University of Waterloo, 1997

[19] Godunov S. K., Ryabenkii V. S., Raznostnye skhemy, Nauka, M., 1973 | Zbl

[20] Marchuk G. I., Metody vychislitelnoi matematiki, Nauka, M., 1980 | MR

[21] Patankar S., Chislennye metody resheniya zadach teploobmena i dinamiki zhidkosti, Energoatomizdat, M., 1984

[22] Loitsyanskii L. G., Mekhanika zhidkosti i gaza, Nauka, M., 1973 | MR