  Three different displacement based finite element formulations over arbitrary
polygons are studied in this paper. The formulations considered are: the
conventional polygonal finite element method (FEM) with Laplace interpolants,
the cell-based smoothed polygonal FEM with simple averaging technique and the
scaled boundary polygon formulation. For the purpose of numerical integration,
we employ the sub-traingulation for the polygonal FEM and classical Gaussian
quadrature for the smoothed FEM and for the scaled boundary polygon
formulation. The accuracy and the convergence properties of these formulations
are studied with a few benchmark problems in the context of linear elasticity
and the linear elastic fracture mechanics. The extension of scaled boundary
polygon to higher order polygons is also discussed.
