99 citations · 430 across the 30 of their papers we have counts for
35 papers
Robust H(curl)-based finite element methods for the incompressible MHD system
Lourenço Beirão da Veiga, Sergio Gómez, Ilaria Perugia +1
We propose and analyze a class of finite element methods for the time-dependent incompressible magnetohydrodynamics system based on -conforming discretizations fo…
Surrogate modeling of resonant behavior in scattering problems through adaptive rational approximation and sketching
Davide Pradovera, Ralf Hiptmair, Ilaria Perugia
This paper describes novel algorithms for the identification of (almost-)resonant behavior in scattering problems. Our methods, relying on rational approximation, aim at building s…
Structure-preserving Local Discontinuous Galerkin method for nonlinear cross-diffusion systems
Sergio Gómez, Ansgar Jüngel, Ilaria Perugia
We present and analyze a structure-preserving method for the approximation of solutions to nonlinear cross-diffusion systems, which combines a Local Discontinuous Galerkin spatial…
On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation
Sergio Gómez, Andrea Moiola, Ilaria Perugia +1
We study the approximation properties of complex-valued polynomial Trefftz spaces for the -dimensional linear time-dependent Schrödinger equation. More precisely, we prove t…
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…
Geometry-based approximation of waves in complex domains
Davide Pradovera, Monica Nonino, Ilaria Perugia
We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. We assume that the wave speed is constant, and tha…
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…
Exponential Convergence of -Time-Stepping in Space-Time Discretizations of Parabolic PDEs
Ilaria Perugia, Christoph Schwab, Marco Zank
For linear parabolic initial-boundary value problems with self-adjoint, time-homogeneous elliptic spatial operator in divergence form with Lipschitz-continuous coefficients, and fo…
On the limiting amplitude principle for the wave equation with variable coefficients
Anton Arnold, Sjoerd Geevers, Ilaria Perugia +1
In this paper, we prove new results on the validity of the limiting amplitude principle (LAP) for the wave equation with nonconstant coefficients, not necessarily in divergence for…
On the exponential time-decay for the one-dimensional wave equation with variable coefficients
Anton Arnold, Sjoerd Geevers, Ilaria Perugia +1
We consider the initial-value problem for the one-dimensional, time-dependent wave equation with positive, Lipschitz continuous coefficients, which are constant outside a bounded r…
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…
An adaptive finite element method for high-frequency scattering problems with smoothly varying coefficients
Anton Arnold, Sjoerd Geevers, Ilaria Perugia +1
We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities.…
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…
A p-robust polygonal discontinuous Galerkin method with minus one stabilization
Silvia Bertoluzza, Ilaria Perugia, Daniele Prada
We introduce a new stabilization for discontinuous Galerkin methods for the Poisson problem on polygonal meshes, which induces optimal convergence rates in the polynomial approxima…
An entropy structure preserving space-time formulation for cross-diffusion systems: Analysis and Galerkin discretization
Marcel Braukhoff, Ilaria Perugia, Paul Stocker
Cross-diffusion systems are systems of nonlinear parabolic partial differential equations that are used to describe dynamical processes in several application, including chemical c…
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…
A polynomial-degree-robust a posteriori error estimator for Nédélec discretizations of magnetostatic problems
Joscha Gedicke, Sjoerd Geevers, Ilaria Perugia +1
We present an equilibration-based a posteriori error estimator for Nédélec element discretizations of the magnetostatic problem. The estimator is obtained by adding a gradient corr…
Space-time discontinuous Galerkin approximation of acoustic waves with point singularities
Pratyuksh Bansal, Andrea Moiola, Ilaria Perugia +1
We develop a convergence theory of space-time discretizations for the linear, 2nd-order wave equation in polygonal domains , possibly occupied by piecewise ho…
An equilibrated a posteriori error estimator for arbitrary-order Nédélec elements for magnetostatic problems
Joscha Gedicke, Sjoerd Geevers, Ilaria Perugia
We present a novel \textit{a posteriori} error estimator for Nédélec elements for magnetostatic problems that is constant-free, i.e. it provides an upper bound on the error that do…
Tent pitching and Trefftz-DG method for the acoustic wave equation
Ilaria Perugia, Joachim Schöberl, Paul Stocker +1
We present a space-time Trefftz discontinuous Galerkin method for approximating the acoustic wave equation semi-explicitly on tent pitched meshes. DG Trefftz methods use discontinu…
A numerical study of the dispersion and dissipation properties of virtual element methods for the Helmholtz problem
Ilaria Perugia, Alexander Pichler
We study numerically the dispersion and dissipation properties of the plane wave virtual element method and the nonconforming Trefftz virtual element method for the Helmholtz probl…
A structure-preserving discontinuous Galerkin scheme for the Fischer-KPP equation
Francesca Bonizzoni, Marcel Braukhoff, Ansgar Jüngel +1
An implicit Euler discontinuous Galerkin scheme for the Fisher-Kolmogorov-Petrovsky-Piscounov (Fisher-KPP) equation for population densities with no-flux boundary conditions is sug…
Robust adaptive hp discontinuous Galerkin finite element methods for the Helmholtz equation
Scott Congreve, Joscha Gedicke, Ilaria Perugia
This paper presents an a posteriori error analysis for the 2D Helmholtz equation that is robust in the polynomial degree and the wave number . For the discretization, w…
Fast Least-Squares Padé approximation of problems with normal operators and meromorphic structure
Francesca Bonizzoni, Fabio Nobile, Ilaria Perugia +1
In this work, we consider the approximation of Hilbert space-valued meromorphic functions that arise as solution maps of parametric PDEs whose operator is the shift of an operator…