Approximation on the hexagonal grid of the Dirichlet problem for Laplace’s equation
Department of Mathematics, Eastern Mediterranean University, Gazimagusa, K.K.T.C., via Mersin, 10, Turkey
Boundary Value Problems 2014, 2014:73 doi:10.1186/1687-2770-2014-73Published: 28 March 2014
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.