Geodesic
A~Method of Composite Grids on a~Prism with an Arbitrary Polygonal Base
Informatics and Automation, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 138-160.

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

The Dirichlet problem for the Laplace equation on a right prism with an arbitrary polygonal base is considered. A method of composite cubic and cylindrical grids is developed that allows one to obtain an approximate solution to this problem. Under certain conditions imposed on the smoothness of boundary values, the uniform convergence with the rate $O(h^2\ln h^{-1})$ is established for a difference solution on a composite grid with the total number of nodes $O(h^{-3}\ln h^{-1})$, where $h$ is the step of a cubic grid. 
@article{TRSPY_2003_243_a11,
     author = {E. A. Volkov},
     title = {A~Method of {Composite} {Grids} on {a~Prism} with an {Arbitrary} {Polygonal} {Base}},
     journal = {Informatics and Automation},
     pages = {138--160},
     publisher = {mathdoc},
     volume = {243},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2003_243_a11/}
}
TY  - JOUR
AU  - E. A. Volkov
TI  - A~Method of Composite Grids on a~Prism with an Arbitrary Polygonal Base
JO  - Informatics and Automation
PY  - 2003
SP  - 138
EP  - 160
VL  - 243
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2003_243_a11/
LA  - ru
ID  - TRSPY_2003_243_a11
ER  - 
%0 Journal Article
%A E. A. Volkov
%T A~Method of Composite Grids on a~Prism with an Arbitrary Polygonal Base
%J Informatics and Automation
%D 2003
%P 138-160
%V 243
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2003_243_a11/
%G ru
%F TRSPY_2003_243_a11
E. A. Volkov. A~Method of Composite Grids on a~Prism with an Arbitrary Polygonal Base. Informatics and Automation, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 138-160. http://geodesic.mathdoc.fr/item/TRSPY_2003_243_a11/

[1] Wasov W., “On the truncation error in the solution of Laplace's equation by finite differences”, J. Res. Nat. Bur. Standards, 48 (1952), 345–348 | MR

[2] Volkov E. A., “O metode regulyarnykh sostavnykh setok dlya uravneniya Laplasa na mnogougolnikakh”, Tr. MIAN, 140, 1976, 68–102 | MR | Zbl

[3] Dosiyev A. A., “A fourth order accurate composite grids method for solving Laplace's boundary value problems with singularities”, ZhVM i MF, 42:6 (2002), 867–884 | MR | Zbl

[4] Volkov E. A., “O differentsialnykh svoistvakh reshenii uravnenii Laplasa i Puassona na parallelepipede i effektivnykh otsenkakh pogreshnosti metoda setok”, Tr. MIAN, 105, 1969, 46–65 | Zbl

[5] Volkov E. A., “Effektivnyi metod kubicheskikh setok resheniya uravneniya Laplasa na parallelepipede pri razryvnykh granichnykh usloviyakh”, Tr. MIAN, 156, 1980, 30–46 | Zbl

[6] Volkov E. A., “On the solution of the Dirichlet problem for the Laplace equation on a rectangular parallelepiped by the grid method”, Russ. J. Numer. Anal. Math. Modelling, 16:6 (2001), 519–527 | MR | Zbl

[7] Volkov E. A., “O gladkosti reshenii zadachi Dirikhle i metode sostavnykh setok na mnogogrannikakh”, Tr. MIAN, 150, 1979, 67–98 | MR | Zbl

[8] Kellog O. D., “On the derivatives of harmonic functions on the boundary”, Trans. Amer. Math. Soc., 33:2 (1931), 486–510 | DOI | MR | Zbl

[9] Miranda K., Uravneniya s chastnymi proizvodnymi ellipticheskogo tipa, IL, M., 1957

[10] Lavrentev M. A., Shabat B. V, Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1987 | MR

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

[12] Keldysh M. V., “O razreshimosti i ustoichivosti zadachi Dirikhle”, UMN, 1941, no. 8, 171–231 | MR | Zbl

[13] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, T. 1, Fizmatlit, M., SPb., 2001