A virtual element method with arbitrary regularity

By L. Beirão da Veiga, Gianmarco Manzini. 2014

171 citations recorded by the source corpus.

and Gianmarco Manzini∗ Los Alamos National Laboratory, Plasma Physics and Applied Mathematics Group, T-5, Theoretical Division, MS B284, Los Alamos, NM 87544, USA and Centro di Simulazione Numerica Avanzata (CeSNA)–IUSS Pavia, v.le Lungo Ticino Sforza 56, I 27100 Pavia, Italy and Istituto di Matematica Applicata e Tecnologie Informatiche (IMATI) – CNR, via Ferrata 1, I 27100 Pavia, Italy ∗Corresponding author: marco.manzini@imati.cnr.it gmanzini@lanl.gov

Subfields: Computational Mechanics, Mechanics of Materials, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ffa8318bd14897705fdfac571fb4d1778eea9103

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Citations in the corpus

Divergence free Virtual Elements for the Stokes problem on polygonal meshes (2015, methodology): “The Virtual Element Method has been applied successfully for a large range of problems, for instance a non exhaustive list being [4, 20, 5, 1, 11, 18, 2, 27, 12, 29, 10, 38, 3].”
Virtual element method for quasilinear elliptic problems (2017, unknown): “ularity assumption used in the linear setting [6, 17], allowing for very general polygonal and polyhedral meshes. Virtual element methods for linear elliptic problems are now well-established, see eg.[6, 11, 1, 10, 5, 17, 13] and [26] for a simple implementation. See also [7] for an extension to mes”
The Hitchhiker's Guide to the Virtual Element Method (2014, methodology): “INTRODUCTION The aim of this paper is to present in detail the practical aspects of the implementation of the Virtual Element Method (VEM) [1, 5, 6, 8, 13, 17].”
Hourglass stabilization and the virtual element method (2015, methodology): “Furthermore, the theory is applicable to C arbitrary-order polygonal and polyhedral elements [16], and also to elements that possess arbitrary regularity [26, 27].”
Conforming and nonconforming virtual element methods for elliptic problems (2015, unknown): “This approach differs completely from that presented for a non-constant diffusion tensor in [11], which required the construction of a bespoke projection operator dependent on the diffusion tensor.”
A Plane Wave Virtual Element Method for the Helmholtz Problem (2015, background): “The basic VEM introduced on the Poisson problem has then been extended to highly regular [11], non conforming [2] and discontinuous approximating spaces [16], to general elliptic [8] and mixed problems [6,7,14], as well as to Stokes [1], plate problems [15], linear and non linear elasticity [5, 10, ”
Some basic formulations of the virtual element method (VEM) for finite deformations (2017, background): “[24, 26, 27, 28, 29, 25, 30, 31, 32, 33]), some attempts have been made for nonlinear [34, 35] and 3D [29] problems.”
A globally conforming method for solving flow in discrete fracture networks using the Virtual Element Method (2016, background): “Further developments can be found in [2], [14], [7] and [6].”
Residual a posteriori error estimation for the Virtual Element Method for elliptic problems (2015, methodology): “As pointed out in reference [9], a better condition number of the stiffness matrix is obtained by scaling the nodal degrees of freedom by an appropriate local mesh size factor.”