Approximation on the hexagonal grid of the Dirichlet problem for Laplace’s equation

被引：0

作者：

Adiguzel A. Dosiyev

Emine Celiker

机构：

[1] Eastern Mediterranean University,Department of Mathematics

来源：

Boundary Value Problems | / 2014卷

关键词：

Laplace’s equation; Dirichlet boundary value problem; hexagonal grids; matching operator; interpolation for harmonic functions; singularity; Block-Grid method;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The fourth order matching operator on the hexagonal grid is constructed. Its application to the interpolation problem of the numerical solution obtained by hexagonal grid approximation of Laplace’s equation on a rectangular domain is investigated. Furthermore, the constructed matching operator is applied to justify a hexagonal version of the combined Block-Grid method for the Dirichlet problem with corner singularity. Numerical examples are illustrated to support the analysis made.

引用

共 50 条

[1] Approximation on the hexagonal grid of the Dirichlet problem for Laplace's equation
Dosiyev, Adiguzel A.
Celiker, Emine
BOUNDARY VALUE PROBLEMS, 2014,
[2] Grid approximation of the first derivatives of the solution to the Dirichlet problem for the Laplace equation on a polygon
E. A. Volkov
Proceedings of the Steklov Institute of Mathematics, 2006, 255 (1)
[3] Uniform approximation by harmonic polynomials for solving the Dirichlet problem of Laplace's equation on a disk
Lee, Haesung
LITHUANIAN MATHEMATICAL JOURNAL, 2025,
[4] A fourth order block-hexagonal grid approximation for the solution of Laplace's equation with singularities
Dosiyev, Adiguzel A.
Celiker, Emine
ADVANCES IN DIFFERENCE EQUATIONS, 2015,
[5] A fourth order block-hexagonal grid approximation for the solution of Laplace’s equation with singularities
Adiguzel A Dosiyev
Emine Celiker
Advances in Difference Equations, 2015
[6] On the solution of the Dirichlet problem for the Laplace equation on a rectangular parallelepiped by the grid method
Volkov, E.A.
Russian Journal of Numerical Analysis and Mathematical Modelling, 2002, 16 (06) : 519 - 527
[7] On the solution of the Dirichlet problem for the Laplace equation on a rectangular parallelepiped by the grid method
Volkov, EA
RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING, 2001, 16 (06) : 519 - 527
[8] Solution of the Dirichlet problem for the Laplace equation
Medková D.
Applications of Mathematics, 1999, 44 (2) : 143 - 168
[9] Dirichlet problem for Laplace-Beltrami equation on hypersurfaces-FEM approximation
Buchukuri, Tengiz
Duduchava, Roland
Tephnadze, George
TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE, 2016, 170 (03) : 300 - 307
[10] On a combined grid method for solving the Dirichlet problem for the Laplace equation in a rectangular parallelepiped
Volkov E.A.
Computational Mathematics and Mathematical Physics, 2007, 47 (4) : 638 - 643

← 1 2 3 4 5 →