The Implement And Super-convergence Research Of Virtual Element Methods Based On Python Language

Virtual element method is developed from mimetic finite difference in recent years.This method is applicable to the general polygon and polyhedral grid,with low requirements about grid quality,even containing some non-convex or multiply-connected polygon grid,which greatly reduces the difficulty of grid generation,so that the method draws much attention from researchers.In this paper,we use the Python language to implement the virtual element method,and explore whether there is super-convergence phenomenon for the virtual element method in the uni-form mesh and CVT grid.Through numerical experiments,the convergence order of H1 error increase 1 nearly comparing with theoretical error convergence order O(h)in the uniform mesh which consists of triangle element or rectangle element,while 0.5 nearly in the CVT grid and uniform grid which consists of polygon element.