CONSTRUCTION OF HEXAGONAL BASIS FUNCTIONS APPLIED IN THE GALERKIN-TYPE FINITE ELEMENT METHOD.

A hexagonal element scheme is formulated to treat the hexagonal lattice together with the Galerkin approximation in finite element method. Presented in this paper is a method of construction of the localized Galerkin functions (shape functions) for a regular hexagon. Here, the shape functions must attain degree one approximation and provide the basis function with the property of inter-element continuity, both of which are inherent in piecewise interpolation. The hexagonal shape functions are constructed as the products of planes on four triangles constituting the hexagon. The functions thus obtained are rational fraction-type and the numerators are the lowest order polynomials within the required conditions.