scholarly journals A stress/displacement Virtual Element method for plane elasticity problems

2017 ◽  
Vol 325 ◽  
pp. 155-174 ◽  
Author(s):  
E. Artioli ◽  
S. de Miranda ◽  
C. Lovadina ◽  
L. Patruno
Keyword(s):  
Plane Elasticity ◽  
Virtual Element Method ◽  
Elasticity Problems ◽  
Virtual Element ◽  
Element Method

scholarly journals A dual hybrid virtual element method for plane elasticity problems

2020 ◽  
Vol 54 (5) ◽  
pp. 1725-1750
Author(s):  
Edoardo Artioli ◽  
Stefano de Miranda ◽  
Carlo Lovadina ◽  
Luca Patruno
Keyword(s):  
Closed Form Solution ◽  
Plane Elasticity ◽  
Form Solution ◽  
Stability And Convergence ◽  
Virtual Element Method ◽  
Convergence Results ◽  
Elasticity Problems ◽  
Virtual Element ◽  
Displacement Based ◽  
Element Method

A dual hybrid Virtual Element scheme for plane linear elastic problems is presented and analysed. In particular, stability and convergence results have been established. The method, which is first order convergent, has been numerically tested on two benchmarks with closed form solution, and on a typical microelectromechanical system. The numerical outcomes have proved that the dual hybrid scheme represents a valid alternative to the more classical low-order displacement-based Virtual Element Method.

The nonconforming virtual element method for elasticity problems

2019 ◽  
Vol 378 ◽  
pp. 394-410 ◽  
Author(s):  
Bei Zhang ◽  
Jikun Zhao ◽  
Yongqin Yang ◽  
Shaochun Chen
Keyword(s):  
Virtual Element Method ◽  
Elasticity Problems ◽  
Virtual Element ◽  
Element Method

scholarly journals Arbitrary-order intrinsic virtual element method for elliptic equations on surfaces

CALCOLO ◽  
2021 ◽  
Vol 58 (3) ◽  
Author(s):  
Elena Bachini ◽  
Gianmarco Manzini ◽  
Mario Putti
Keyword(s):  
Arbitrary Order ◽  
Surface Geometry ◽  
Virtual Element Method ◽  
Anisotropic Character ◽  
Local Reference System ◽  
Local Reference ◽  
Local Parametrization ◽  
Manufactured Solution ◽  
Virtual Element ◽  
Element Method

AbstractWe develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in covariant form using an appropriate local reference system. The knowledge of the local parametrization allows us to consider the two-dimensional VEM scheme, without any explicit approximation of the surface geometry. The theoretical properties of the classical VEM are extended to our framework by taking into consideration the highly anisotropic character of the final discretization. These properties are extensively tested on triangular and polygonal meshes using a manufactured solution. The limitations of the scheme are verified as functions of the regularity of the surface and its approximation.

Non-conforming Harmonic Virtual Element Method: $$h$$ h - and $$p$$ p -Versions

2018 ◽  
Vol 77 (3) ◽  
pp. 1874-1908 ◽  
Author(s):  
Lorenzo Mascotto ◽  
Ilaria Perugia ◽  
Alexander Pichler
Keyword(s):  
Virtual Element Method ◽  
Virtual Element ◽  
Element Method

scholarly journals The virtual element method for resistive magnetohydrodynamics

2021 ◽  
Vol 381 ◽  
pp. 113815
Author(s):  
S. Naranjo Alvarez ◽  
V. Bokil ◽  
V. Gyrya ◽  
G. Manzini
Keyword(s):  
Virtual Element Method ◽  
Virtual Element ◽  
Element Method
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