The nonconforming virtual element method

Publikationstyp
Journal Article
Date Issued
2016-05-01
Sprache
English
Author(s)
Ayuso De Dios, Blanca  
Lipnikov, Konstantin  
Manzini, Gianmarco  
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/6151
Journal
ESAIM: Mathematical Modelling and Numerical Analysis  
Volume
50
Issue
3
Start Page
879
End Page
904
Citation
ESAIM: Mathematical Modelling and Numerical Analysis 3 (50): 879-904 (2016-05-01)
Publisher DOI
10.1051/m2an/2015090
Scopus ID
2-s2.0-84971420023
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.
Subjects
Elliptic problems
Nonconforming method
Poisson equation
Unstructured meshes
Virtual element method