8 citations · 17 across the 7 of their papers we have counts for
9 papers · 1 filter
Error estimates for a helicity-preserving finite element discretisation of an incompressible magnetohydrodynamics system
L. Beirao da Veiga, K. Hu, L. Mascotto
We derive error estimates of a finite element method for the approximation of solutions to a seven-fields formulation of a magnetohydrodynamics model, which preserves the energy of…
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…
Interpolation and stability estimates for edge and face virtual elements of general order
Lourenço Beirão da Veiga, Lorenzo Mascotto, Jian Meng
We develop interpolation error estimates for general order standard and serendipity edge and face virtual elements in two and three dimensions. Contextually, we investigate the sta…
Virtual elements for Maxwell's equations
L. Beirão da Veiga, F. Dassi, G. Manzini +1
We present a low order virtual element discretization for time dependent Maxwell's equations, which allow for the use of general polyhedral meshes. Both the semi- and fully-discret…
Interpolation and stability properties of low order face and edge virtual element spaces
Lourenço Beirão da Veiga, Lorenzo Mascotto
We analyse the interpolation properties of 2D and 3D low order virtual element face and edge spaces, which generalize Nédélec and Raviart-Thomas polynomials to polygonal-polyhedral…
p- and hp- virtual elements for the Stokes problem
Alexey Chernov, Carlo Marcati, Lorenzo Mascotto
We analyse the p- and hp-versions of the virtual element method (VEM) for the the Stokes problem on a polygonal domain. The key tool in the analysis is the existence of a bijection…
The harmonic virtual element method: stabilization and exponential convergence for the Laplace problem on polygonal domains
Alexey Chernov, Lorenzo Mascotto
We introduce the harmonic virtual element method (harmonic VEM), a modification of the virtual element method (VEM) for the approximation of the 2D Laplace equation using polygonal…
Exponential convergence of the hp Virtual Element Method with corner singularities
Lorenzo Mascotto, Lourenço Beirão da Veiga, Alexey Chernov +1
In the present work, we analyze the version of Virtual Element methods for the 2D Poisson problem. We prove exponential convergence of the energy error employing sequences of…
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…