Lowest order stabilization free Virtual Element Method for the Poisson equation

03/31/2021

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by   Stefano Berrone, et al.

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We introduce and analyse the first order Enlarged Enhancement Virtual Element Method (E^2VEM) 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.