Lowest order stabilization free virtual element method for the 2D Poisson equation
Year: 2024
Type: article
Abstract: We analyze 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 property (from which comes the prefix E 2 ) of local virtual spaces. We provide a sufficient condition for the well-posedness and optimal order a priori error estimates. We present numerical tests on convex and non-convex polygonal meshes that confirm the robustness of the method and the theoretical convergence rates.
Institution: Politecnico di Torino
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,310
Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Politecnico di Torino, Dipartimenti di Eccellenza, European Commission, Ministero dell’Istruzione, dell’Università e della Ricerca, Ministero dell'Università e della Ricerca, Gruppo Nazionale per il Calcolo Scientifico, Division of Mathematical Sciences
OpenAlex ID: W4404515082