40 citations · 130 across the 21 of their papers we have counts for
23 papers
The High Order Virtual Element Method On Approximate Domains: Neumann Boundary Conditions
Silvia Bertoluzza, Monica Montardini, Daniele Prada
In the framework of the virtual element method with shifted boundary type treatment of curved geometries, we propose a novel approach to the treatment of Neumann boundary condition…
The MINI mixed virtual element for the Stokes equation
Silvia Bertoluzza, Fabio Credali, Daniele Prada
We present and discuss a generalization of the popular MINI mixed finite element for the 2D Stokes equation by means of conforming virtual elements on polygonal meshes. We prove op…
Reduced basis stabilization and post-processing for the virtual element method
Fabio Credali, Silvia Bertoluzza, Daniele Prada
We present a reduced basis method for cheaply constructing (possibly rough) approximations to the nodal basis functions of the virtual element space, and propose to use such approx…
Best approximation results and essential boundary conditions for novel types of weak adversarial network discretizations for PDEs
Silvia Bertoluzza, Erik Burman, Cuiyu He
In this paper, we provide a theoretical analysis of the recently introduced weakly adversarial networks (WAN) method, used to approximate partial differential equations in high dim…
Artificial neural network evaluation of geometric constants for polygonal domains
Beatrice Crippa, Sofia Imperatore, Silvia Bertoluzza +1
We propose an approach based on Artificial Neural Networks (ANNs) to evaluate geometric constants relevant to the analysis and design of numerical schemes for partial differential…
The virtual element method on polygonal pixel-based tessellations
Silvia Bertoluzza, Monica Montardini, Micol Pennacchio +1
We analyze and validate the virtual element method combined with a boundary correction similar to the one in [1,2], to solve problems on two dimensional domains with curved boundar…