Lowest order stabilization free Virtual Element Method for the 2D Poisson equation

Abstract

We introduce and analyse the first order Enlarged Enhancement Virtual Element Method (E${}^2$VEM) 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 (from which comes the prefix of the name E${}^2$) property of local virtual spaces. The polynomial degree of local projections is chosen based on the number of vertices of each polygon. 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 criterium for well-posedness and the theoretical convergence rates.

arXiv comment35 pages, 8 figures

References in corpus (4)

• A Virtual Element Method for elastic and inelastic problems on polytope meshes
• SUPG stabilization for the nonconforming virtual element method for advection-diffusion-reaction equations
• Stabilization-free serendipity virtual element method for plane elasticity
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Cited by in corpus (2)

• A residual a posteriori error estimate for the Stabilization-free Virtual Element Method
• Benchmarking stabilized and self-stabilized p-virtual element methods with variable coefficients