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

Michael Mengolini; Matías F. Benedetto; Alejandro M. Aragón

doi:10.1016/j.cma.2019.02.043

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

Michael Mengolini, Matías F. Benedetto, Alejandro M. Aragón^*

^*Corresponding author for this work

Computational Design and Mechanics

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53 Citations (Scopus)

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Abstract

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.

Original language	English
Pages (from-to)	995-1023
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	350
DOIs	https://doi.org/10.1016/j.cma.2019.02.043
Publication status	Published - 2019

Keywords

FEM
Linear elasticity
Non-conforming meshes
p-FEM
Stress recovery
VEM

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10.1016/j.cma.2019.02.043

1-s2.0-S0045782519301215-mainFinal published version, 2.57 MBLicence: CC BY

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title = "An engineering perspective to the virtual element method and its interplay with the standard finite element method",

abstract = "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.",

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AU - Mengolini, Michael

AU - Benedetto, Matías F.

AU - Aragón, Alejandro M.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - FEM

KW - Linear elasticity

KW - Non-conforming meshes

KW - p-FEM

KW - Stress recovery

KW - VEM

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DO - 10.1016/j.cma.2019.02.043

M3 - Article

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SN - 0045-7825

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SP - 995

EP - 1023

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -

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

Abstract

Keywords

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