An engineering perspective to the virtual element method and its interplay with the standard finite element method

In this manuscript we thoroughly study the behavior of the virtual element method (VEM) in the context of two-dimensional linear elasticity problems for an engineering audience versed in standard FEM. Through detailed convergence studies we show the accuracy and the convergence rates recovered by VE...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2019-06, Vol.350, p.995-1023
Main Authors: Mengolini, Michael, Benedetto, Matías F., Aragón, Alejandro M.
Format: Article
Language:English
Subjects:
[formula omitted]-FEM
Convergence
Elasticity
FEM
Finite element analysis
Finite element method
Linear elasticity
Mathematical analysis
Non-conforming meshes
Nonlinear programming
Stress recovery
VEM
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Summary:In this manuscript we thoroughly study the behavior of the virtual element method (VEM) in the context of two-dimensional linear elasticity problems for an engineering audience versed in standard FEM. Through detailed convergence studies we show the accuracy and the convergence rates recovered by VEM, and we compare them to those obtained by the h- and p-versions of the finite element method (FEM). We also demonstrate the mixability between FEM and VEM; in particular, applications of VEM for coupling non-conforming discretizations and for local refinement are presented, showing higher versatility compared to FEM. Computer implementation aspects in displacement-based finite element codes are thoroughly explained, remarking on the main differences with respect to standard FEM. •A practical exposition of the Virtual Element Method (VEM) for linear elastostatics;•VEM’s advantages and disadvantages are discussed and compared to both h- and p-FEM;•The method’s performance is thoroughly studied for smooth and non-smooth problems;•VEM’s versatility as a helper method to FEM in a hybrid approach is demonstrated;•Implementation aspects of VEM in displacement-based FEM packages are discussed.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2019.02.043