Basic principles of Virtual Element Methods

By L. Beir, Franco Brezzi, Saudi Arabia. 2013

1,439 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/5e87b309b41f42e6e1a6fed3a0b7ac6f717d3759

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. L. Beirão da Veiga
2. Gianmarco Manzini
3. Giuseppe Vacca
4. Alessandro Russo
5. Glaucio H. Paulino
6. Carlo Lovadina
7. Paola Francesca Antonietti
8. Natarajan Sukumar

In Computational Theory and Mathematics

1. L. Beirão da Veiga
2. Gianmarco Manzini
3. Alessandro Russo
4. Giuseppe Vacca
5. Glaucio H. Paulino
6. Carlo Lovadina
7. Joseph E. Bishop
8. Paola Francesca Antonietti

In Mechanics of Materials

1. Gianmarco Manzini
2. L. Beirão da Veiga
3. Alessandro Russo
4. Giuseppe Vacca
5. Glaucio H. Paulino
6. Carlo Lovadina
7. Natarajan Sukumar
8. Andrea Cangiani

Citations in the corpus

• The Virtual Element Method with curved edges (2017, methodology): “In order to compute the VEM errors between the exact solution uex and VEM solution uh, we consider the computable error quantities: errH1 := (∑ E∈Ωh ∥∥∥∇uex −∇(Π∇,Ek uh)∥∥∥20,E )1/2 |uex|1 , errL2 := (∑ E∈Ωh ∥∥∥uex −Π∇,Ek uh∥∥∥20,E )1/2 ‖uex‖0 .”
• Topology optimization using polytopes (2013, methodology): “We make a computationally inexpensive choice as [5]: s(u,v) = n ∑”
• A Plane Wave Virtual Element Method for the Helmholtz Problem (2015, methodology): “. 65N30, 65N12, 65N15, 35J05. Thedateswillbesetbythepublisher. Introduction The Virtual Element Method (in short, VEM) is a generalization of the classical finite element method recently introduced in [4,9]. The key features of the VEM are: • the decomposition of the computational domain can consist ”
• On the Virtual Element Method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes (2013, background): “This, in turn, implies that the element E can represent rigid body motions and states of constant strain, i.e.,”
• A virtual element method with arbitrary regularity (2014, methodology): “We refer the interested reader to Beirão da Veiga et al. (2013) for a thorough discussion concerning this issue.”
• New perspectives on polygonal and polyhedral finite element methods (2014, methodology): “A posteriori estimators for the mimetic discretizations appear in References [125, 126], and high-order mimetic discretizations are developed in References [127, 128, 129].”
• Hourglass stabilization and the virtual element method (2015, methodology): “Herein, we show that the recently proposed virtual element method [16], coined as VEM, can be viewed as a generalized hourglass stabilization technique for arbitrary-order polygonal and polyhedral finite element methods.”