Geodesic
Grid Approximation of the First Derivatives of the Solution to the Dirichlet Problem for the Laplace Equation on a Polygon
Informatics and Automation, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 99-115 
E. A. Volkov. Grid Approximation of the First Derivatives of the Solution to the Dirichlet Problem for the Laplace Equation on a Polygon. Informatics and Automation, Function spaces, approximation theory, and nonlinear analysis, Tome 255 (2006), pp. 99-115. http://geodesic.mathdoc.fr/item/TRSPY_2006_255_a7/
@article{TRSPY_2006_255_a7,
     author = {E. A. Volkov},
     title = {Grid {Approximation} of the {First} {Derivatives} of the {Solution} to the {Dirichlet} {Problem} for the {Laplace} {Equation} on {a~Polygon}},
     journal = {Informatics and Automation},
     pages = {99--115},
     year = {2006},
     volume = {255},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2006_255_a7/}
}
TY  - JOUR
AU  - E. A. Volkov
TI  - Grid Approximation of the First Derivatives of the Solution to the Dirichlet Problem for the Laplace Equation on a Polygon
JO  - Informatics and Automation
PY  - 2006
SP  - 99
EP  - 115
VL  - 255
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2006_255_a7/
LA  - ru
ID  - TRSPY_2006_255_a7
ER  - 
%0 Journal Article
%A E. A. Volkov
%T Grid Approximation of the First Derivatives of the Solution to the Dirichlet Problem for the Laplace Equation on a Polygon
%J Informatics and Automation
%D 2006
%P 99-115
%V 255
%U http://geodesic.mathdoc.fr/item/TRSPY_2006_255_a7/
%G ru
%F TRSPY_2006_255_a7

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

Using the method of composite square and polar grids, we construct approximations of the first derivatives of the solution to the Dirichlet problem for the Laplace equation on a polygon and find error estimates for such approximations.

[1] Volkov E.A., “Metod sostavnykh setok dlya konechnykh i beskonechnykh oblastei s kusochno gladkoi granitsei”, Tr. MIAN, 96, 1968, 117–148 | Zbl

[2] Volkov E.A., “O differentsialnykh svoistvakh reshenii kraevykh zadach dlya uravneniya Laplasa na mnogougolnikakh”, Tr. MIAN, 77, 1965, 113–142 | Zbl

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

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

[5] Volkov E.A., Dosiev A.A., Bozer M., “Metod sostavnykh setok povyshennoi tochnosti”, DAN, 396:4 (2004), 446–448 | MR | Zbl

[6] Volkov E.A., “O differentsialnykh svoistvakh reshenii kraevykh zadach dlya uravnenii Laplasa i Puassona na pryamougolnike”, Tr. MIAN, 77, 1965, 89–112 | Zbl

[7] Volkov E.A., “Effektivnye otsenki pogreshnosti reshenii metodom setok kraevykh zadach dlya uravnenii Laplasa i Puassona na pryamougolnike i nekotorykh treugolnikakh”, Tr. MIAN, 74, 1966, 55–85 | Zbl

[8] Stechkin S.B., “Dopolnenie VI”, Khardi G.G., Littlvud Dzh.E., Polia G., Neravenstva, Izd-vo inostr. lit., M., 1948, 388–393

[9] Volkov E.A., “On convergence in $C_2$ of a difference solution of the Laplace equation on a rectangle”, Russ. J. Numer. Anal. and Math. Modell., 14:3 (1999), 291–298 | DOI | MR | Zbl

[10] Bakhvalov N.S., Zhidkov N.P., Kobelkov G.M., Chislennye metody, Binom. Laboratoriya znanii, M., 2004, 636 pp.

[11] Volkov E.A., “Priblizhennoe reshenie uravnenii Laplasa i Puassona v vesovykh prostranstvakh Geldera”, Tr. MIAN, 128, 1972, 76–112 | Zbl

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

[13] Miranda K., Uravneniya s chastnymi proizvodnymi ellipticheskogo tipa, Izd-vo inostr. lit., M., 1957, 256 pp.

[14] Samarskii A.A., Andreev V.B., Raznostnye metody dlya ellipticheskikh uravnenii, Nauka, M., 1976, 352 pp. | MR | Zbl