Ilaria Perugia

An arbitrarily high-order accurate and locally energy/entropy-stable space-time method for a class of nonlinear wave systems

Michael Dumbser, Ilaria Perugia, Enrico Zampa

We present a new class of structure-preserving, arbitrarily high-order accurate space-time schemes using unstructured simplicial meshes in space for a class of nonlinear acoustic w…

A space-time sparse-grid method for the wave equation

Matteo Ferrari, Andrea Moiola, Chiara Perinati +1

We develop a fast space-time numerical scheme for approximating solutions to the linear wave equation. The approach is based on the sparse-grid combination technique applied to a c…

A Multilevel Monte Carlo Virtual Element Method for Uncertainty Quantification of Elliptic Partial Differential Equations

Paola F. Antonietti, Francesca Bonizzoni, Ilaria Perugia +1

We introduce a Monte Carlo Virtual Element estimator based on Virtual Element discretizations for stochastic elliptic partial differential equations with random diffusion coefficie…

Stability, convergence, and geometric properties of second-order-in-time space-time discretizations for linear and semilinear wave equations

Matteo Ferrari, Ilaria Perugia, Enrico Zampa

We revisit second-order-in-time space-time discretizations of the linear and semilinear wave equations by establishing precise equivalences with first-order-in-time formulations. F…

Structure-preserving local discontinuous Galerkin discretization of conformational conversion systems

Paola F. Antonietti, Mattia Corti, Sergio Gómez +1

We investigate a two-state conformational conversion system and introduce a novel structure-preserving numerical scheme that couples a local discontinuous Galerkin space discretiza…

Inf-sup stable space-time discretization of the wave equation based on a first-order-in-time variational formulation

Matteo Ferrari, Ilaria Perugia, Enrico Zampa

In this paper, we present a conforming space-time discretization of the wave equation based on a first-order-in-time variational formulation with exponential weights in time. We an…

A structure-preserving LDG discretization of the Fisher-Kolmogorov equation for modeling neurodegenerative diseases

Paola F. Antonietti, Mattia Corti, Sergio Gómez +1

This work presents a structure-preserving, high-order, unconditionally stable numerical method for approximating the solution to the Fisher-Kolmogorov equation on polytopic meshes,…

Intrinsic unconditional stability in space-time isogeometric approximation of the acoustic wave equation in second-order formulation

Matteo Ferrari, Ilaria Perugia

We present a novel space-time isogeometric discretization of the acoustic wave equation in second-order formulation that is intrinsically unconditionally stable. The method relies…

Symplectic QTT-FEM solution of the one-dimensional acoustic wave equation in the time domain

Sara Fraschini, Vladimir Kazeev, Ilaria Perugia

Structured Finite Element Methods (FEMs) based on low-rank approximation in the form of the so-called Quantized Tensor Train (QTT) decomposition (QTT-FEM) have been proposed and ex…

Unconditionally stable space-time isogeometric discretization for the wave equation in Hamiltonian formulation

Matteo Ferrari, Sara Fraschini, Gabriele Loli +1

We consider a family of conforming space-time discretizations for the wave equation based on a first-order-in-time formulation employing maximal regularity splines. In contrast wit…

A Nonconforming Virtual Element Method for Advection-Diffusion-Reaction Problems with CIP Stabilization

Carlo Lovadina, Ilaria Perugia, Manuel Trezzi

We study a nonconforming virtual element method (VEM) for advection-diffusion-reaction problems with continuous interior penalty (CIP) stabilization. The design of the method is ba…