73 citations · 364 across the 42 of their papers we have counts for
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Annotations on the virtual element method for second-order elliptic problems
Gianmarco Manzini
This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document…
Convergence analysis of the mimetic finite difference method for elliptic problems with staggered discretization of the diffusion coefficients
G. Manzini, K. Lipnikov, J. D. Moulton +1
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, t…
Convergence of spectral discretizations of the Vlasov-Poisson system
Gianmarco Manzini, Daniele Funaro, Gian Luca Delzanno
We prove the convergence of a spectral discretization of the Vlasov-Poisson system. The velocity term of the Vlasov equation is discretized using either Hermite functions on the in…
The fully nonconforming virtual element method for biharmonic problems
P. F. Antonietti, G. Manzini, M. Verani
In this paper we address the numerical approximation of linear fourth-order elliptic problems on polygonal meshes. In particular, we present a novel nonconforming virtual element d…
Discretization of mixed formulations of elliptic problems on polyhedral meshes
Konstantin Lipnikov, Gianmarco Manzini
We review basic design principles underpinning the construction of mimetic finite difference and a few finite volume and finite element schemes for mixed formulations of elliptic p…
A Legendre-Fourier spectral method with exact conservation laws for the Vlasov-Poisson system
G. Manzini, G. L. Delzanno, J. Vencels +1
We present the design and implementation of an L2-stable spectral method for the discretization of the Vlasov- Poisson model of a collisionless plasma in one space and velocity dim…
The non-conforming virtual element method for the Stokes equations
Andrea Cangiani, Vitaliy Gyrya, Gianmarco Manzini
We present the non-conforming Virtual Element Method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using…