A first-order stabilization-free Virtual Element Method. (August 2023) - Berrone, Stefano; Borio, Andrea; Marcon, Francesca; Teora, Gioana
Abstract: In this paper, we introduce a new Virtual Element Method (VEM) not requiring any stabilization term based on the usual enhanced first-order VEM space. The new method relies on a modified formulation of the discrete diffusion operator that ensures stability preserving all the properties of the differential operator. Highlights: A new first-order stabilization-free VEM based on an unchanged VEM space. This approach provides an operator preserving VEM bilinear form. The method is based on projections on spaces of harmonic polynomials. The paper numerically discuss stability and convergence issues.