75 citations · 304 across the 24 of their papers we have counts for
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math.NA2022★ 1 cited
A posteriori error analysis and adaptivity for a VEM discretization of the Navier-Stokes equations
Claudio Canuto, Davide Rosso
We consider the Virtual Element method (VEM) introduced by Beirão da Veiga, Lovadina and Vacca in 2016 for the numerical solution of the steady, incompressible Navier-Stokes equati…
math.NA2022★ 67 cited
Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks
S. Berrone, C. Canuto, M. Pintore +1
In this paper, we present and compare four methods to enforce Dirichlet boundary conditions in Physics-Informed Neural Networks (PINNs) and Variational Physics-Informed Neural Netw…
math.NA2022★ 29 cited
Solving PDEs by Variational Physics-Informed Neural Networks: an a posteriori error analysis
Stefano Berrone, Claudio Canuto, Moreno Pintore
We consider the discretization of elliptic boundary-value problems by variational physics-informed neural networks (VPINNs), in which test functions are continuous, piecewise linea…