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The Hitchhiker's Guide to the Virtual Element Method

Mathematical Models and Methods in Applied Sciences, 2014
We present the essential ingredients in the Virtual Element Method for a simple linear elliptic second-order problem. We emphasize its computer implementation, which will enable interested readers to readily implement the method.
L Beirao da Veiga   +3 more
openaire   +6 more sources

Virtual Element Method: Micro-Mechanics Applications

Key Engineering Materials, 2019
In this contribution we present an application of the lowest order Virtual Element Method (VEM) to the problem of material computational homogenization. Material homogenization allows retrieving material properties through suitable volume averaging procedures, starting from a detailed representation of the micro-constituents of the considered material.
Marco Lo Cascio   +2 more
openaire   +1 more source

A virtual element method for contact

Computational Mechanics, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wriggers, P., Rust, W. T., Reddy, B. D.
openaire   +2 more sources

Equivalent projectors for virtual element methods

Computers & Mathematics with Applications, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
B Ahmad   +4 more
openaire   +2 more sources

Virtual element method for the Sobolev equations

Mathematical Methods in the Applied Sciences, 2022
The virtual element method for the Sobolev equations is proposed in this paper, where the semi‐discrete scheme and the fully discrete scheme are both discussed. With the help of the energy projection operator defined by the discrete bilinear form, the corresponding optimal error estimates in the norm and semi‐norm for both the semi‐discrete ...
Buying Zhang, Jikun Zhao, Shaochun Chen
openaire   +1 more source

Shape optimization with virtual element method

Communications in Nonlinear Science and Numerical Simulation
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Feng, Fang, Yang, Hui, Zhu, Shengfeng
openaire   +1 more source

Virtual Element and Discontinuous Galerkin Methods

2013
Virtual element methods (VEM) are the latest evolution of the Mimetic Finite Difference Method and can be considered to be more close to the Finite Element approach. They combine the ductility of mimetic finite differences for dealing with rather weird element geometries with the simplicity of implementation of Finite Elements.
F Brezzi, LD Marini
openaire   +2 more sources

A Novel Polygonal Finite Element Method: Virtual Node Method

AIP Conference Proceedings, 2010
Polygonal finite element method (PFEM), which can construct shape functions on polygonal elements, provides greater flexibility in mesh generation. However, the non‐polynomial form of traditional PFEM, such as Wachspress method and Mean Value method, leads to inexact numerical integration. Since the integration technique for non‐polynomial functions is
X. H. Tang   +6 more
openaire   +1 more source

Magnetic resonance linear accelerator technology and adaptive radiation therapy: An overview for clinicians

Ca-A Cancer Journal for Clinicians, 2022
William A Hal, X Allen Li, Daniel A Low
exaly  

Virtual Tumor Board: Papillary thyroid carcinoma with nodal disease

Ca-A Cancer Journal for Clinicians, 2023
Peter J Abraham
exaly  

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