The nonconforming virtual element method

¹ Institut für Mathematik, Technische Universität Hamburg-Harburg, Am Schwarzenberg-Campus 3, D-21073 Hamburg, Germany
blanca.ayuso@tuhh.de
² Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI) – CNR, 27100 Pavia, Italy
marco.manzini@imati.cnr.it
³ Applied Mathematics and Plasma Physics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
lipnikov@lanl.gov; gmanzini@lanl.gov

Received: 26 April 2015
Revised: 2 November 2015

Abstract

We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the conforming VEM and the classical nonconforming finite element methods. We provide the error analysis and establish the equivalence with a family of mimetic finite difference methods. Numerical experiments verify the theory and validate the performance of the proposed method.