1 citations · 1 across the 6 of their papers we have counts for
7 papers
Finite element exterior calculus for spectra and pseudospectra of advection-diffusion of differential forms
Daniele Boffi, Kaibo Hu, Yizhou Liang +1
Numerical investigations of dynamo action have remained active in fluid mechanics over the past decades, presenting numerous challenges and open problems. Meanwhile, the developmen…
Achieving Material Robustness via Symmetric Stress Finite Element Discretizations
Pablo Brubeck, Charles Parker, Umberto Zerbinati
When discretizing symmetric stress tensors in variational problems arising in continuum mechanics, one has to choose how to enforce the symmetry of the stress tensor: (i) strongly…
Preconditioned normal equations for solving discretised partial differential equations
Lorenzo Lazzarino, Yuji Nakatsukasa, Umberto Zerbinati
This paper explores preconditioning the normal equation for non-symmetric square linear systems arising from PDE discretization, focusing on methods like CGNE and LSQR. The concept…
A comparison of the Coco-Russo scheme and $\protect\mathghost$-FEM for elliptic equations in arbitrary domains
Clarissa Astuto, Armando Coco, Umberto Zerbinati
In this paper, a comparative study between the Coco-Russo scheme (based on finite-difference scheme) and the $\mathghost$-FEM (based on finite-element method) is presented when sol…
An adaptive mesh refinement strategy to ensure quasi-optimality of finite element methods for self-adjoint Helmholtz problems
Tim van Beeck, Umberto Zerbinati
It is well known that the quasi-optimality of the Galerkin finite element method for the Helmholtz equation is dependent on the mesh size and the wave-number. In the literature, di…
A nodal ghost method based on variational formulation and regular square grid for elliptic problems on arbitrary domains in two space dimensions
Clarissa Astuto, Daniele Boffi, Giovanni Russo +1
This paper focuses on the numerical solution of elliptic partial differential equations (PDEs) with Dirichlet and mixed boundary conditions, specifically addressing the challenges…
PINNs and GaLS: A Priori Error Estimates for Shallow Physics Informed Neural Networks Applied to Elliptic Problems
Umberto Zerbinati
Physics Informed Neural Networks (PINNs) have recently gained popularity for solving partial differential equations, given the fact they escape the curse of dimensionality. In this…