7 papers
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…
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…