Abstract: The irrational function forms interpolation on a polygonal element with arbitrary nodal distribution was constructed by using mean value coordinates of polygonal elements. The polygonal finite element method for solving boundary value problems of differential equations was presented. For a curved boundary, the polygonal meshes can exactly approximate the arbitrary geometric shape by proper nodal distribution. The expressions of shape function within different elements are uniform. It is convenient to program the computer codes for finite element analysis. Numerical examples on second order elliptical boundary value problems are presented to demonstrate the accuracy and effectiveness of the proposed method.

Key words: irrational function interpolation, polygonal element, polygonal finite element method, barycentric coordinates, mean value coordinates