Comparison of standard and stabilization free Virtual Elements on anisotropic elliptic problems

Abstract: In this letter we compare the behaviour of standard Virtual Element Methods (VEM) and stabilization free Enlarged Enhancement Virtual Element Methods (E$^2$VEM) with the focus on some elliptic test problems whose solution and diffusivity tensor are characterized by anisotropies. Results show that the possibility to avoid an arbitrary stabilizing part, offered by E$^2$VEM methods, can reduce the magnitude of the error on general polygonal meshes and help convergence.