Comparison of Standard and Stabilization Free Virtual Elements on Anisotropic Elliptic Problems.

In this letter we compare the behaviour of standard Virtual Element Methods (VEM) and stabilization free Enlarged Enhancement Virtual Element Methods (E2V EM) 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 E2V EM methods, can reduce the magnitude of the error on general polygonal meshes and help convergence.