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Open Access Research

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

Adiguzel A Dosiyev* and Emine Celiker

Author Affiliations

Department of Mathematics, Eastern Mediterranean University, Gazimagusa, K.K.T.C., via Mersin, 10, Turkey

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Boundary Value Problems 2014, 2014:73  doi:10.1186/1687-2770-2014-73

Published: 28 March 2014

Abstract

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.

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