In this paper, we propose and analyze a Stabilization Free Virtual Element Method (SFVEM), that allows the definition of bilinear forms that do not require an arbitrary stabilization term, thanks to the exploitation of higher-order polynomial projections on divergence free vectors of polynomials. The method is introduced in the lowest order formulation for the Poisson problem. We provide a sufficient condition on the polynomial projection space that implies the well-posedness, proved on particular classes of polygons, and optimal order a priori error estimates. Numerical tests on convex and non-convex polygonal meshes confirm the theoretical convergence rates and show that the method is suitable for solving problems characterized by anisotropies.
A stabilization-free Virtual Element Method based on divergence-free projections / Berrone, Stefano; Borio, Andrea; Marcon, Francesca. - In: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING. - ISSN 0045-7825. - ELETTRONICO. - 424:(2024), pp. 1-19. [10.1016/j.cma.2024.116885]
A stabilization-free Virtual Element Method based on divergence-free projections
Berrone, Stefano;Borio, Andrea;Marcon, Francesca
2024
Abstract
In this paper, we propose and analyze a Stabilization Free Virtual Element Method (SFVEM), that allows the definition of bilinear forms that do not require an arbitrary stabilization term, thanks to the exploitation of higher-order polynomial projections on divergence free vectors of polynomials. The method is introduced in the lowest order formulation for the Poisson problem. We provide a sufficient condition on the polynomial projection space that implies the well-posedness, proved on particular classes of polygons, and optimal order a priori error estimates. Numerical tests on convex and non-convex polygonal meshes confirm the theoretical convergence rates and show that the method is suitable for solving problems characterized by anisotropies.File | Dimensione | Formato | |
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https://hdl.handle.net/11583/2986479