Stabilization-free Virtual Element Method for 2D second order elliptic equations

• DOI: 10.1016/j.cma.2025.117839
• Publication Date: 2025-02-16T19:32:07Z
• Authors: Stefano Berrone; Andrea Borio; Davide Fassino; Francesca Marcon

In this work, we present and analyze a Stabilization-free Virtual Element high order scheme for 2D second order elliptic equation. This method is characterized by the definition of new polynomial projections that allow the definition of structure-preserving schemes. We provide a necessary and sufficient condition on the polynomial projection space that ensure the well-posedness of the scheme and we derive optimal a priori error estimates. Several numerical tests assess the stability of the method and the robustness in solving problems characterized by anisotropies.