Incompressible Fluid Computation Based on Polygonal Finite Element

This paper, instead of using the popular numerical methods such as Finite Element Method, Finite Volume Method, etc. that are applied for fluid computation with the advantages of simplicity, introduces a new method named Polygonal Finite Element Method (PFEM). Based on the stability of mixed finite element, discretization is governed by the so-called inf-sup condition, which, in this case, depends on the choice of the discrete velocity and pressure spaces. We put forward a new choice of these spaces defined over convex polygonal partitions of the domain. Within each element, the pressure field is represented by the polygonal basis functions and the velocity is controlled by richer polygonal bubble functions.