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…
Interior estimates for the Virtual Element Method
Silvia Bertoluzza, Micol Pennacchio, Daniele Prada
We analyze the local accuracy of the virtual element method. More precisely, we prove an error bound similar to the one holding for the finite element method, namely, that the loca…
Weakly imposed Dirichlet boundary conditions for 2D and 3D Virtual Elements
Silvia Bertoluzza, Micol Pennacchio, Daniele Prada
In the framework of virtual element discretizazions, we address the problem of imposing non homogeneous Dirichlet boundary conditions in a weak form, both on polygonal/polyhedral d…
A theoretical and numerical analysis of a Dirichlet-Neumann domain decomposition method for diffusion problems in heterogeneous media
Alex Viguerie, Silvia Bertoluzza, Alessandro Veneziani +1
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in le…
Stabilization of the nonconforming virtual element method
Silvia Bertoluzza, Gianmarco Manzini, Micol Pennacchio +1
We address the issue of designing robust stabilization terms for the nonconforming virtual element method. To this end, we transfer the problem of defining the stabilizing bilinear…
VEM and the Mesh
Tommaso Sorgente, Daniele Prada, Daniela Cabiddu +6
In this work we report some results, obtained within the framework of the ERC Project CHANGE, on the impact on the performance of the virtual element method of the shape of the pol…
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 a posteriori error estimate of the outer normal derivative using dual weights
Silvia Bertoluzza, Erik Burman, Cuiyu He
We derive a residual based a-posteriori error estimate for the outer normal flux of approximations to {the diffusion problem with variable coefficient}. By analyzing the solution o…
The Virtual Element Method for a Minimal Surface Problem
Paola Francesca Antonietti, Silvia Bertoluzza, Daniele Prada +1
In this paper we consider the Virtual Element discretization of a minimal surface problem, a quasi-linear elliptic partial differential equation modeling the problem of minimizing…
A Fat boundary-type method for localized nonhomogeneous material problems
Alex Viguerie, Silvia Bertoluzza, Ferdinando Auricchio
Problems with localized nonhomogeneous material properties arise frequently in many applications and are a well-known source of difficulty in numerical simulations. In certain appl…
Algebraic representation of dual scalar products and stabilization of saddle point problems
Silvia Bertoluzza
We provide a systematic way to design computable bilinear forms which, on the class of subspaces that can be obtained by duality from a given finite di…
Benchmark of Polygon Quality Metrics for Polytopal Element Methods
M. Attene, S. Biasotti, S. Bertoluzza +6
Polytopal Element Methods (PEM) allow to solve differential equations on general polygonal and polyhedral grids, potentially offering great flexibility to mesh generation algorithm…
FETI-DP for the three-dimensional Virtual Element Method
Silvia Bertoluzza, Micol Pennacchio, Daniele Prada
We deal with the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) preconditioner for elliptic problems discretized by the virtual element method (VEM). We extend th…
High order VEM on curved domains
Silvia Bertoluzza, Micol Pennacchio, Daniele Prada
We deal with the virtual element method (VEM) for solving the Poisson equation on a domain with curved boundaries. Given a polygonal approximation of the domain , the…
A Polygonal Discontinuous Galerkin Method with Minus One Stabilization
Silvia Bertoluzza, Daniele Prada
We propose a Discontinuous Galerkin method for the Poisson equation on polygonal tessellations in two dimensions, stabilized by penalizing, locally in each element , a residual…
FETI-DP preconditioners for the Virtual Element Method on general 2D meshes
Daniele Prada, Silvia Bertoluzza, Micol Pennacchio +1
We analyze the performance of a state-of-the-art domain decomposition approach, the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) method, for the efficient solut…
BDDC and FETI-DP for the Virtual Element Method
Silvia Bertoluzza, Micol Pennacchio, Daniele Prada
We build and analyze Balancing Domain Decomposition by Constraint (BDDC) and Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) preconditioners for elliptic problems…
Local Error Estimates of the Finite Element Method for an Elliptic Problem with a Dirac Source Term
Silvia Bertoluzza, Astrid Decoene, Loïc Lacouture +1
The solutions of elliptic problems with a Dirac measure in right-hand side are not H1 and therefore the convergence of the finite element solutions is suboptimal. Graded meshes are…