scholarly journals A family of virtual element methods for plane elasticity problems based on the Hellinger–Reissner principle

2018 ◽  
Vol 340 ◽  
pp. 978-999 ◽  
Author(s):  
E. Artioli ◽  
S. de Miranda ◽  
C. Lovadina ◽  
L. Patruno
Keyword(s):  
Plane Elasticity ◽  
Elasticity Problems ◽  
Virtual Element Methods ◽  
Virtual Element

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.

scholarly journals Robust nonconforming virtual element methods for general fourth-order problems with varying coefficients

2021 ◽  
Author(s):  
Andreas Dedner ◽  
Alice Hodson
Keyword(s):  
Fourth Order ◽  
Perturbation Parameter ◽  
Two Dimensions ◽  
Optimal Error Estimates ◽  
Projection Operators ◽  
Varying Coefficients ◽  
Virtual Element Methods ◽  
Virtual Element ◽  
Perturbation Problems ◽  
Fourth Order Problems

Abstract We present a class of nonconforming virtual element methods for general fourth-order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual element spaces. Optimal error estimates in the energy norm are provided for general linear fourth-order problems with varying coefficients. We also discuss fourth-order perturbation problems and present a novel nonconforming scheme which is uniformly convergent with respect to the perturbation parameter without requiring an enlargement of the space. Numerical tests are carried out to verify the theoretical results. We conclude with a brief discussion on how our approach can easily be applied to nonlinear fourth-order problems.

Some Estimates for Virtual Element Methods

2017 ◽  
Vol 17 (4) ◽  
pp. 553-574 ◽  
Author(s):  
Susanne C. Brenner ◽  
Qingguang Guan ◽  
Li-Yeng Sung
Keyword(s):  
Error Estimates ◽  
Three Dimensions ◽  
Poisson Problem ◽  
Polyhedral Meshes ◽  
Virtual Element Methods ◽  
Virtual Element

AbstractWe present novel techniques for obtaining the basic estimates of virtual element methods in terms of the shape regularity of polygonal/polyhedral meshes. We also derive new error estimates for the Poisson problem in two and three dimensions.

Solution of plane elasticity problems with Mathematica

1995 ◽  
Vol 55 (2) ◽  
pp. 229-236 ◽  
Author(s):  
N.I. Ioakimidis ◽  
G.T. Anastasselos
Keyword(s):  
Plane Elasticity ◽  
Elasticity Problems
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