scholarly journals Lowest-order virtual element methods for linear elasticity problems

2022 ◽  
Vol 390 ◽  
pp. 114448
Author(s):  
Do Y. Kwak ◽  
Hyeokjoo Park
Keyword(s):  
Linear Elasticity ◽  
Elasticity Problems ◽  
Virtual Element Methods ◽  
Virtual Element

A low-order locking-free virtual element for linear elasticity problems

2020 ◽  
Vol 80 (5) ◽  
pp. 1260-1274
Author(s):  
Xialan Tang ◽  
Zhibin Liu ◽  
Baiju Zhang ◽  
Minfu Feng
Keyword(s):  
Linear Elasticity ◽  
Elasticity Problems ◽  
Virtual Element ◽  
Low Order

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.

The Boundary Contour Method for Three-Dimensional Linear Elasticity

1996 ◽  
Vol 63 (2) ◽  
pp. 278-286 ◽  
Author(s):  
A. Nagarajan ◽  
S. Mukherjee ◽  
E. Lutz
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Linear Elasticity ◽  
Three Dimensional ◽  
Contour Method ◽  
Boundary Contour ◽  
Boundary Contour Method ◽  
Novel Variant ◽  
Elasticity Problems ◽  
Element Method

This paper presents a novel variant of the boundary element method, here called the boundary contour method, applied to three-dimensional problems of linear elasticity. In this work, the surface integrals on boundary elements of the usual boundary element method are transformed, through an application of Stokes’ theorem, into line integrals on the bounding contours of these elements. Thus, in this formulation, only line integrals have to be numerically evaluated for three-dimensional elasticity problems—even for curved surface elements of arbitrary shape. Numerical results are presented for some three-dimensional problems, and these are compared against analytical solutions.

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