A VEM–based mesh–adaptive strategy for potential problems

The Virtual Element Method (VEM) is an evolution of the mimetic finite difference method which overcomes many limitations affecting classic Finite Element Methods (FEM). VEM for 2D problems allows for exploiting meshes consisting of any polygonal elements. No limitations on their internal angles are needed. Hanging nodes are easily treated. Notably, VEM is well apt to mesh–adaptive algorithms. In this paper we detail an implementation of mesh–adaptive VEM for potential problems. We suggest a fresh, promising approach. We show on suitable test problems that a gain in efficiency can be obtained, respect to uniform, fine discretizations.