Results 251 to 260 of about 18,745,540 (280)

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.
Alessandro Russo, Luisa Donatella Marini, Franco Brezzi   +2 more
exaly   +8 more sources

The NonConforming Virtual Element Method for the Stokes Equations [PDF]

SIAM Journal on Numerical Analysis, 2016
We present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space.
Vitaliy Gyrya, Andrea Cangiani, Gianmarco Manzini   +2 more
exaly   +12 more sources

The Role of Stabilization in the Virtual Element Method: A Survey

Computers and Mathematics With Applications, 2023
The virtual element method was introduced 10 years ago and it has generated a large number of theoretical results and applications ever since. Here, we overview the main mathematical results concerning the stabilization term of the method as an introduction for newcomers in the field.
Lorenzo Mascotto
exaly   +7 more sources

A Virtual Element Method for Isotropic Hyperelasticity [PDF]

Computer Methods in Applied Mechanics and Engineering, 2020
This work considers the application of the virtual element method to plane hyperelasticity problems with a novel approach to the selection of stabilization parameters. The method is applied to a range of numerical examples and well known strain energy functions, including neo-Hookean, Mooney-Rivlin and Ogden material models.
Daniel van Huyssteen
exaly   +5 more sources

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Equivalent Projectors for Virtual Element Methods

Computers and Mathematics With Applications, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bashir Ahmad, Alessandro Russo, Ahmed Alsaedi   +2 more
exaly   +3 more sources

Conforming Virtual Element Methods for Sobolev Equations

Journal of Scientific Computing, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yang Xu 0014, Zhenguo Zhou, Jingjun Zhao
openaire   +1 more source

Some Estimates for Virtual Element Methods

Computational Methods in Applied Mathematics, 2017
Abstract We 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.
Susanne C. Brenner, Qingguang Guan, Li-Yeng Sung   +2 more
openaire   +3 more sources

The Mixed Virtual Element Method for the Richards Equation

2021
The time-dependent Richards equation can be reformulated as a nonlinear, possibly degenerate, parabolic problem in mixed form by applying the Kirchhoff transformation. A preliminary time integration yields the variational formulation. A numerical treatment of this problem using polygonal and polyhedral meshes is, then, feasible by applying themixed ...
D Adak, G Manzini, S Natarajan
openaire   +3 more sources

An adaptive virtual element method for incompressible flow

Computers & Mathematics with Applications, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ying Wang 0026, Gang Wang 0054, Feng Wang 0030   +2 more
openaire   +3 more sources

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