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

Boundary value problems

Emine Celiker¹  Adiguzel A. Dosiyev¹ 

[1] Department of Mathematics, Eastern Mediterranean University, Turkey

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

DOI  :  10.1186/1687-2770-2014-73

学科分类：数学（综合）

来源: SpringerOpen

【 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. MSC:35A35, 35A40, 35C15, 65N06, 65N15, 65N22, 65N99.

【 授权许可】

CC BY