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

T Vu-Huu,Q Hoan Pham,M Abdel-Wahab,Sy Pham-Van,C Le-Thanh,H Nguyen-Xuan

doi:10.1088/1742-6596/1777/1/012065

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.

Highlights

Nowadays, among many potential numerical methods, e.g., finite volume method, smooth particle hydrodynamics, finite difference method, or finite element method; polygonal finite element method (PFEM) is emerging as the most interesting method for fluid flow computations because of its special benefits in the good accuracy and high flexibility
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
It can be performed on almost mesh families, i.e., triangular, quadrilateral, random Voronoi mesh, etc

Summary

Introduction

Among many potential numerical methods, e.g., finite volume method, smooth particle hydrodynamics, finite difference method, or finite element method (see Refs. [1,2,3,4]); polygonal finite element method (PFEM) is emerging as the most interesting method for fluid flow computations because of its special benefits in the good accuracy and high flexibility. [1,2,3,4]); polygonal finite element method (PFEM) is emerging as the most interesting method for fluid flow computations because of its special benefits in the good accuracy and high flexibility It can be performed on almost mesh families, i.e., triangular, quadrilateral, random Voronoi mesh, etc. Three kinds of error norms, i.e., the error of velocity, euL2, error of pressure, epL2, in the approximation space L2-norm and the velocity gradient error, euH1, in the approximation space H1 -norm are deployed to assess the convergence rate of Pe1Pe1 Another interested evaluation of the CPU time of the proposed PFE is executed as well.

Stoke governing equation system

Polygonal discretisation system

Numerical tests

Conclusion