An equal-order mixed polygonal finite element for two-dimensional incompressible Stokes flows

Abstract

Abstract In this study, a novel equal-order mixed polygonal finite element is developed to solve the incompressible fluid problems. Our developed element, so-called Pe1Pe1, is established by the system of polygonal basis functions for both fluid pressure and velocity fields. The superiority of the present formulation over the existent low-order polygonal element is its full applicability in all arbitrary polygonal mesh families. Furthermore, our element provides a better approximation solution for pressure field in fluid analysis. To avoid the well-known instability in equal-order mixed discretizations, we develop an adequate stabilization method, which is extremely effective, yet simple, to improve the numerical performance of our polygonal finite element. In this research, the quality of the present approach with respect to the convergence rate and its stability is presented by a variety of numerical samples of the incompressible Stokes flow problems.