Lowest order stabilization free Virtual Element Method for the Poisson equation

Abstract

We introduce and analyse the first order Enlarged Enhancement Virtual Element Method (E$^2$VEM) for the Poisson problem. The method has the interesting property of allowing the definition of bilinear forms that do not require a stabilization term. We provide a proof of well-posedness and optimal order a priori error estimates. Numerical tests on convex and non-convex polygonal meshes confirm the theoretical convergence rates.