Lowest order stabilization free virtual element method for the 2D Poisson equation

We analyze the first order Enlarged Enhancement Virtual Element Method (E2VEM) for the Poisson problem. The method allows the definition of bilinear forms that do not require a stabilization term, thanks to the exploitation of higher order polynomial projections that are made computable by suitably enlarging the enhancement property (from which comes the prefix E2) of local virtual spaces. We provide a sufficient condition for the well-posedness and optimal order a priori error estimates. We present numerical tests on convex and non-convex polygonal meshes that confirm the robustness of the method and the theoretical convergence rates.