The hybrid high-order method for polytopal meshes
DA Di Pietro, J Droniou - Number 19 in Modeling, Simulation and …, 2020 - Springer
Originally introduced in [146, 158], Hybrid High-Order (HHO) methods provide a framework
for the discretisation of models based on Partial Differential Equations (PDEs) with features …
for the discretisation of models based on Partial Differential Equations (PDEs) with features …
A review on arbitrarily regular conforming virtual element methods for second-and higher-order elliptic partial differential equations
The virtual element method is well suited to the formulation of arbitrarily regular Galerkin
approximations of elliptic partial differential equations of order 2 p 1, for any integer p 1≥ 1 …
approximations of elliptic partial differential equations of order 2 p 1, for any integer p 1≥ 1 …
Stability analysis for the virtual element method
L Beirão da Veiga, C Lovadina… - Mathematical Models and …, 2017 - World Scientific
We analyze the virtual element methods (VEM) on a simple elliptic model problem, allowing
for more general meshes than the one typically considered in the VEM literature. For …
for more general meshes than the one typically considered in the VEM literature. For …
Conforming and nonconforming virtual element methods for elliptic problems
We present, in a unified framework, new conforming and nonconforming virtual element
methods for general second-order elliptic problems in two and three dimensions. The …
methods for general second-order elliptic problems in two and three dimensions. The …
A posteriori error estimates for the virtual element method
An posteriori error analysis for the virtual element method (VEM) applied to general elliptic
problems is presented. The resulting error estimator is of residual-type and applies on very …
problems is presented. The resulting error estimator is of residual-type and applies on very …
Arbitrary order 2D virtual elements for polygonal meshes: part I, elastic problem
E Artioli, L Beirão da Veiga, C Lovadina… - Computational …, 2017 - Springer
The present work deals with the formulation of a virtual element method for two dimensional
structural problems. The contribution is split in two parts: in part I, the elastic problem is …
structural problems. The contribution is split in two parts: in part I, the elastic problem is …
A review of hybrid high-order methods: formulations, computational aspects, comparison with other methods
DA Di Pietro, A Ern, S Lemaire - … and challenges in modern approaches to …, 2016 - Springer
Abstract Hybrid High-Order (HHO) methods are formulated in terms of discrete unknowns
attached to mesh faces and cells (hence, the term hybrid), and these unknowns are …
attached to mesh faces and cells (hence, the term hybrid), and these unknowns are …
A stress/displacement virtual element method for plane elasticity problems
E Artioli, S De Miranda, C Lovadina… - Computer Methods in …, 2017 - Elsevier
The numerical approximation of 2D elasticity problems is considered, in the framework of the
small strain theory and in connection with the mixed Hellinger–Reissner variational …
small strain theory and in connection with the mixed Hellinger–Reissner variational …
An -conforming virtual element for Darcy and Brinkman equations
G Vacca - Mathematical Models and Methods in Applied …, 2018 - World Scientific
The focus of this paper is on developing a virtual element method (VEM) for Darcy and
Brinkman equations. In [L. Beirão da Veiga, C. Lovadina and G. Vacca, ESAIM Math. Model …
Brinkman equations. In [L. Beirão da Veiga, C. Lovadina and G. Vacca, ESAIM Math. Model …
Ill‐conditioning in the virtual element method: Stabilizations and bases
L Mascotto - Numerical Methods for Partial Differential …, 2018 - Wiley Online Library
In this article, we investigate the behavior of the condition number of the stiffness matrix
resulting from the approximation of a 2D Poisson problem by means of the virtual element …
resulting from the approximation of a 2D Poisson problem by means of the virtual element …