The convergence rate of a polygonal finite element for Stokes flows on different mesh families

Abstract

Abstract This paper introduces an evaluation to consider the convergence rate of a polygonal finite element (PFE) to solve two-dimensional (2D) incompressible steady Stokes flows on different mesh families. For this purpose, a numerical example of 2D incompressible steady Stokes flows programmed and coded by MATLAB is deployed. Furthermore, the mixed equal-order PFE, i.e., Pe1Pe1, is utilised for this research. Additionally, five different mesh families, i.e., triangular, quadrilateral, hexagonal, random Voronoi, centroidal Voronoi meshes, are applied for this research. Moreover, an interesting evaluation of the CPU time for the performance of our proposed PFE in this research is employed as well. From these tests, differences in convergence rate, as well as CPU time of using Pe1Pe1 on different mesh families, are indicated.