A high-order mixed polygonal finite element for incompressible Stokes flow analysis

Abstract

This paper presents a new high-order mixed scheme of polygonal finite element method (PFEM) for incompressible flow computation. The system of polygonal basis functions with bubble-enriched functions is applied to represent the fluid velocity field, while the pressure field is approximated by the set of polygonal basis functions. The new element is named as MINIPe. From a practical point of view, the present element naturally satisfies the well-known inf–sup condition. The numerical tests of the incompressible fluid flow problems governed by Stokes equation systems are presented to verify the performance quality of proposed method with respect to the stability and convergence rate.