20 citations · 80 across the 33 of their papers we have counts for
38 papers
Iterative solution to the biharmonic equation in mixed form discretized by the Hybrid High-Order method
Paola F. Antonietti, Pierre Matalon, Marco Verani
We consider the solution to the biharmonic equation in mixed form discretized by the Hybrid High-Order (HHO) methods. The two resulting second-order elliptic problems can be decoup…
A DG-VEM method for the dissipative wave equation
Paola Francesca Antonietti, Francesca Bonizzoni, Marco Verani
A novel space-time discretization for the (linear) scalar-valued dissipative wave equation is presented. It is a structured approach, namely, the discretization space is obtained t…
Optimized numerical solutions of SIRDVW multiage model controlling SARS-CoV-2 vaccine roll out: an application to the Italian scenario
Giovanni Ziarelli, Luca Dede', Nicola Parolini +2
In the context of SARS-CoV-2 pandemic, mathematical modelling has played a fundamental role for making forecasts, simulating scenarios and evaluating the impact of preventive polit…
Virtual Element Method for the Navier--Stokes Equation coupled with the Heat Equation
Paola Francesca Antonietti, Giuseppe Vacca, Marco Verani
We consider the Virtual Element discretization of the Navier-Stokes equations coupled with the heat equation where the viscosity depends on the temperature. We present the Virtual…
Non-isothermal non-Newtonian fluids: the stationary case
Maurizio Grasselli, Nicola Parolini, Andrea Poiatti +1
The stationary Navier-Stokes equations for a non-Newtonian incompressible fluid are coupled with the stationary heat equation and subject to Dirichlet type boundary conditions. The…
Identification of cavities and inclusions in linear elasticity with a phase-field approach
Andrea Aspri, Elena Beretta, Cecilia Cavaterra +2
In this paper, we deal with the inverse problem of the shape reconstruction of cavities and inclusions embedded in a linear elastic isotropic medium from boundary displacement's me…
-VEM for some variants of the Cahn-Hilliard equation: a numerical exploration
Paola F. Antonietti, Simone Scacchi, Giuseppe Vacca +1
We consider the -Virtual Element Method (VEM) for the conforming numerical approximation of some variants of the Cahn-Hilliard equation on polygonal meshes. In particular, we…
On arbitrarily regular conforming virtual element methods for elliptic partial differential equations
Paola Francesca Antonietti, Gianmarco Manzini, Simone Scacchi +1
The Virtual Element Method (VEM) is a very effective framework to design numerical approximations with high global regularity to the solutions of elliptic partial differential equa…
Agglomeration-based geometric multigrid schemes for the Virtual Element Method
Paola Francesca Antonietti, Stefano Berrone, Martina Busetto +1
In this paper we analyse the convergence properties of two-level, W-cycle and V-cycle agglomeration-based geometric multigrid schemes for the numerical solution of the linear syste…
A review on arbitrarily regular conforming virtual element methods for elliptic partial differential equations
Paola Francesca Antonietti, Gianmarco Manzini, Simone Scacchi +1
The Virtual Element Method is well suited to the formulation of arbitrarily regular Galerkin approximations of elliptic partial differential equations of order , for any inte…
The conforming virtual element method for polyharmonic and elastodynamics problems: a review
Paola Francesca Antonietti, Gianmarco Manzini, Ilario Mazzieri +2
In this paper, we review recent results on the conforming virtual element approximation of polyharmonic and elastodynamics problems. The structure and the content of this review is…
A diffuse interface box method for elliptic problems
G. Negrini, N. Parolini, M. Verani
We introduce a diffuse interface box method (DIBM) for the numerical approximation on complex geometries of elliptic problems with Dirichlet boundary conditions. We derive a priori…
Stability analysis of polytopic Discontinuous Galerkin approximations of the Stokes problem with applications to fluid-structure interaction problems
Paola F. Antonietti, Lorenzo Mascotto, Marco Verani +1
We present a stability analysis of the Discontinuous Galerkin method on polygonal and polyhedral meshes (PolyDG) for the Stokes problem. In particular, we analyze the discrete inf-…
Polytopic Discontinuous Galerkin methods for the numerical modelling of flow in porous media with networks of intersecting fractures
Paola Francesca Antonietti, Chiara Facciolà, Marco Verani
We present a numerical approximation of Darcy's flow through a porous medium that incorporates networks of fractures with non empty intersection. Our scheme employs PolyDG methods,…
Anisotropic a posteriori error estimate for the Virtual Element Method
Paola Francesca Antonietti, Stefano Berrone, Andrea Borio +3
We derive an anisotropic a posteriori error estimate for the adaptive conforming Virtual Element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we…
The Virtual Element Method for a Minimal Surface Problem
Paola Francesca Antonietti, Silvia Bertoluzza, Daniele Prada +1
In this paper we consider the Virtual Element discretization of a minimal surface problem, a quasi-linear elliptic partial differential equation modeling the problem of minimizing…
The virtual element method for linear elastodynamics models. Convergence, stability and dissipation-dispersion analysis
P. F. Antonietti, G. Manzini, I. Mazzieri +2
We design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi-discre…
A posteriori error estimates for the monodomain model in cardiac electrophysiology
Luca Ratti, Marco Verani
We consider the monodomain model, a system of a parabolic semilinear reaction-diffusion equation coupled with a nonlinear ordinary differential equation, arising from the (simplifi…
The conforming virtual element method for polyharmonic problems
P. F. Antonietti, G. Manzini, M. Verani
In this work, we exploit the capability of virtual element methods in accommodating approximation spaces featuring high-order continuity to numerically approximate differential pro…
A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square
Claudio Canuto, Ricardo H. Nochetto, Rob Stevenson +1
Both practice and analysis of adaptive -FEMs and -FEMs raise the question what increment in the current polynomial degree guarantees a -independent reduction of the G…
Optimal control in ink-jet printing via instantaneous control
Ivan Fumagalli, Nicola Parolini, Marco Verani
This paper concerns the optimal control of a free surface flow with moving contact line, inspired by an application in ink-jet printing. Surface tension, contact angle and wall fri…
Topology optimization of multiple anisotropic materials, with application to self-assembling diblock copolymers
Francesco Regazzoni, Nicola Parolini, Marco Verani
We propose a solution strategy for a multimaterial minimum compliance topology optimization problem, which consists in finding the optimal allocation of a finite number of candidat…
A phase-field approach for the interface reconstruction in a nonlinear elliptic problem arising from cardiac electrophysiology
Elena Beretta, Luca Ratti, Marco Verani
In this work we tackle the reconstruction of discontinuous coefficients in a semilinear elliptic equation from the knowledge of the solution on the boundary of the domain, an inver…
A multigrid algorithm for the -version of the Virtual Element Method
P. F. Antonietti, L. Mascotto, M. Verani
We present a multigrid algorithm for the solution of the linear systems of equations stemming from the version of the Virtual Element discretization of a two-dimensional Poisso…