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.
Ayuso De Dios, B., Lipnikov, K., Manzini, G. (2016). The nonconforming virtual element method. MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE, 50(3), 879-904 [10.1051/m2an/2015090].
The nonconforming virtual element method
Ayuso De Dios, B
;
2016
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.
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nonc_vemVersion4GGOct29-1.pdf
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NcVem_published.pdf
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