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arXiv · 2103.16896

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

Stefano Berrone·Andrea Borio·Francesca Marcon
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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.

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Stefano Berrone, Andrea Borio, Francesca Marcon. 2021-03-31. Lowest order stabilization free Virtual Element Method for the 2D Poisson equation. https://doi.org/10.1016/j.camwa.2024.11.017

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