Volume 50, Number 3, May-June 2016
Special Issue – Polyhedral discretization for PDE
|Page(s)||879 - 904|
|Published online||23 May 2016|
The nonconforming virtual element method
Institut für Mathematik, Technische Universität
Schwarzenberg-Campus 3, D-21073
2 Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI) – CNR, 27100 Pavia, Italy
3 Applied Mathematics and Plasma Physics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Received: 26 April 2015
Revised: 2 November 2015
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.
Mathematics Subject Classification: 65N30 / 65N12 / 65G99 / 76R99
Key words: Virtual element method / nonconforming method / Poisson equation / elliptic problems / unstructured meshes
© EDP Sciences, SMAI 2016
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