286 citations · 540 across the 16 of their papers we have counts for
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The nonconforming virtual element method with curved edges
Lourenco Beirão Da Veiga, Yi Liu, Lorenzo Mascotto +1
We introduce a nonconforming virtual element method for the Poisson equation on domains with curved boundary and internal interfaces. We prove arbitrary order optimal convergence i…
Stability and interpolation properties for Stokes-like virtual element spaces
L. Beirão da Veiga, L. Mascotto, J. Meng
We prove stability bounds for Stokes-like virtual element spaces in two and three dimensions. Such bounds are also instrumental in deriving optimal interpolation estimates. Further…
The Stokes complex for Virtual Elements in three dimensions
L. Beirao da Veiga, F. Dassi, G. Vacca
The present paper has two objectives. On one side, we develop and test numerically divergence free Virtual Elements in three dimensions, for variable ``polynomial'' order. These ar…
The Stokes complex for Virtual Elements with application to Navier--Stokes flows
L. Beirão da Veiga, D. Mora, G. Vacca
In the present paper, we investigate the underlying Stokes complex structure of the Virtual Element Method for Stokes and Navier--Stokes introduced in previous papers by the same a…
The Virtual Element Method with curved edges
L. Beirão da Veiga, A. Russo, G. Vacca
In this paper we initiate the investigation of Virtual Elements with curved faces. We consider the case of a fixed curved boundary in two dimensions, as it happens in the approxima…
Lowest order Virtual Element approximation of magnetostatic problems
L. Beirão da Veiga, F. Brezzi, F. Dassi +2
We give here a simplified presentation of the lowest order Serendipity Virtual Element method, and show its use for the numerical solution of linear magneto-static problems in thre…
Arbitrary order 2D virtual elements for polygonal meshes: Part II, inelastic problem
Edoardo Artioli, Lourenco Beirão da Veiga, Carlo Lovadina +1
The present paper is the second part of a twofold work, whose first part is reported in [3], concerning a newly developed Virtual Element Method (VEM) for 2D continuum problems. Th…
Arbitrary order 2D virtual elements for polygonal meshes: Part I, elastic problem
Edoardo Artioli, Lourenco Beirao da Veiga, Carlo Lovadina +1
The present work deals with the formulation of a Virtual Element Method (VEM) for two dimensional structural problems. The contribution is split in two parts: in part I, the elasti…
A virtual element method for the acoustic vibration problem
Lourenço Beirão da Veiga, David Mora, Gonzalo Rivera +1
We analyze in this paper a virtual element approximation for the acoustic vibration problem. We consider a variational formulation relying only on the fluid displacement and propos…
Serendipity Nodal VEM spaces
L. Beirao da Veiga, F. Brezzi, L. D. Marini +1
We introduce a new variant of Nodal Virtual Element spaces that mimics the "Serendipity Finite Element Methods" (whose most popular example is the 8-node quadrilateral) and allows…
Basic principles of hp Virtual Elements on quasiuniform meshes
L. Beirão da Veiga, A. Chernov, L. Mascotto +1
In the present paper we initiate the study of Virtual Elements. We focus on the case with uniform polynomial degree across the mesh and derive theoretical convergence estimate…
A Virtual Element Method for elastic and inelastic problems on polytope meshes
L. Beirão da Veiga, C. Lovadina, D. Mora
We present a Virtual Element Method (VEM) for possibly nonlinear elastic and inelastic problems, mainly focusing on a small deformation regime. The numerical scheme is based on a l…
Virtual Element Methods for general second order elliptic problems on polygonal meshes
L. Beirão da Veiga, F. Brezzi, L. D. Marini +1
We consider the discretization of a boundary value problem for a general linear second-order elliptic operator with smooth coefficients using the Virtual Element approach. As in [5…
H(div) and H(curl)-conforming VEM
L. Beirao da Veiga, F. Brezzi, L. D. Marini +1
In the present paper we construct Virtual Element Spaces that are -conforming and -conforming on general polygonal and polyhedral elements; these s…
Numerical results for mimetic discretization of Reissner-Mindlin plate problems
Lourenco Beirao da Veiga, Carlo Lovadina, David Mora
A low-order mimetic finite difference (MFD) method for Reissner-Mindlin plate problems is considered. Together with the source problem, the free vibration and the buckling problems…
An isogeometric method for the Reissner-Mindlin plate bending problem
L. Beirão da Veiga, A. Buffa, C. Lovadina +2
We present a new isogeometric method for the discretization of the Reissner-Mindlin plate bending problem. The proposed scheme follows a recent theoretical framework that makes pos…