38 citations · 122 across the 17 of their papers we have counts for
18 papers
Stability and interpolation estimates of Hellinger-Reissner virtual element spaces
Michele Botti, Lorenzo Mascotto, Giuseppe Vacca +1
We prove stability and interpolation estimates for Hellinger-Reissner virtual elements; the constants appearing in such estimates only depend on the aspect ratio of the polytope un…
Design and performance of a space-time virtual element method for the heat equation on prismatic meshes
Sergio Gómez, Lorenzo Mascotto, Ilaria Perugia
We present a space-time virtual element method for the discretization of the heat equation, which is defined on general prismatic meshes and variable degrees of accuracy. Strategie…
The role of stabilization in the virtual element method: a survey
L. Mascotto
The virtual element method was introduced 10 years ago and it has generated a large number of theoretical results and applications ever since. Here, we overview the main mathematic…
Space-time virtual elements for the heat equation
Sergio Gómez, Lorenzo Mascotto, Andrea Moiola +1
We propose and analyze a space-time virtual element method for the discretization of the heat equation in a space-time cylinder, based on a standard Petrov-Galerkin formulation. Lo…
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 Virtual Element Method for the 3D Resistive Magnetohydrodynamic model
Lourenço Beirão da Veiga, Franco Dassi, Gianmarco Manzini +1
We present a four-field Virtual Element discretization for the time-dependent resistive Magnetohydrodynamics equations in three space dimensions, focusing on the semi-discrete form…
Adaptive virtual elements based on hybridized, reliable, and efficient flux reconstructions
F. Dassi, J. Gedicke, L. Mascotto
We present two a posteriori error estimators for the virtual element method (VEM) based on global and local flux reconstruction in the spirit of [5]. The proposed error estimators…
Mortar coupling of -discontinuous Galerkin and boundary element methods for the Helmholtz equation
Christoph Erath, Lorenzo Mascotto, Jens Markus Melenk +2
We design and analyze a coupling of a discontinuous Galerkin finite element method with a boundary element method to solve the Helmholtz equation with variable coefficients in thre…
The nonconforming Trefftz virtual element method: general setting, applications, and dispersion analysis for the Helmholtz equation
L. Mascotto, I. Perugia, A. Pichler
We present a survey of the nonconforming Trefftz virtual element method for the Laplace and Helmholtz equations. For the latter, we present a new abstract analysis, based on weaker…
FEM-BEM mortar coupling for the Helmholtz problem in three dimensions
Lorenzo Mascotto, Jens Markus Melenk, Ilaria Perugia +1
We present a FEM-BEM coupling strategy for time-harmonic acoustic scattering in media with variable sound speed. The coupling is realized with the aid of a mortar variable that is…
Adaptive virtual element methods with equilibrated fluxes
Franco Dassi, Joscha Gedicke, Lorenzo Mascotto
We present an hp-adaptive virtual element method (VEM) based on the hypercircle method of Prager and Synge for the approximation of solutions to diffusion problems. We introduce a…
The - and -versions of the virtual element method for elliptic eigenvalue problems
O. Certik, F. Gardini, G. Manzini +2
We discuss the - and the -versions of the virtual element method for the approximation of eigenpairs of elliptic operators with a potential term on polygonal meshes. An appl…
Extension of the nonconforming Trefftz virtual element method to the Helmholtz problem with piecewise constant wave number
L. Mascotto, A. Pichler
We extend the nonconforming Trefftz virtual element method introduced in arXiv:1805.05634 to the case of the fluid-fluid interface problem, that is, a Helmholtz problem with piecew…
A nonconforming Trefftz virtual element method for the Helmholtz problem: numerical aspects
L. Mascotto, I. Perugia, A. Pichler
We discuss the implementation details and the numerical performance of the recently introduced nonconforming Trefftz virtual element method for the 2D Helmholtz problem. In particu…
A nonconforming Trefftz virtual element method for the Helmholtz problem
L. Mascotto, I. Perugia, A. Pichler
We introduce a novel virtual element method (VEM) for the two dimensional Helmholtz problem endowed with impedance boundary conditions. Local approximation spaces consist of Trefft…
A posteriori error estimation and adaptivity in virtual elements
L. Beirão da Veiga, G. Manzini, L. Mascotto
An explicit and computable error estimator for the version of the virtual element method (VEM), together with lower and upper bounds with respect to the exact energy error, is…
Non-conforming harmonic virtual element method: - and -versions
Lorenzo Mascotto, Ilaria Perugia, Alexander Pichler
We study the - and -versions of non-conforming harmonic virtual element methods (VEM) for the approximation of the Dirichlet-Laplace problem on a 2D polygonal domain, providi…
Exploring High-order three dimensional Virtual Elements: bases and stabilizations
Lorenzo Mascotto, Franco Dassi
We present numerical tests of the Virtual Element Method (VEM) tailored for the discretization of a three dimensional Poisson problem with high-order "polynomial" degree (up to $p=…