9 citations · 17 across the 10 of their papers we have counts for
11 papers
Conforming and non-conforming virtual element methods for the biharmonic Steklov eigenvalue problem with minimum regularity
Dibyendu Adak, Daniele Boffi, Francesca Gardini +2
In this work, we analyze the conforming and -non-conforming Virtual Element Method for a fourth-order Steklov eigenvalue problem on a generally shaped, possibly nonconvex, pol…
Virtual element approximation of eigenvalue problems: is the stabilization of the right hand side necessary?
Daniele Boffi, Francesca Gardini, Lucia Gastaldi
The VEM approximation of eigenvalue problems usually involves the appropriate tuning of stabilization parameters, unless self-stabilizing or stabilization-free VEM are used. In thi…
Avoiding stabilization terms in virtual elements for eigenvalue problems: The Reduced Basis Virtual Element Method
Silvia Bertoluzza, Fabio Credali, Francesca Gardini
We present the novel Reduced Basis Virtual Element Method (rbVEM) for solving the Laplace eigenvalue problem. This approach is based on the lowest-order virtual element method and…
Virtual element approximation of eigenvalue problems
Daniele Boffi, Francesca Gardini, Lucia Gastaldi
We discuss the approximation of eigenvalue problems associated with elliptic partial differential equations using the virtual element method. After recalling the abstract theory, w…
Approximation of PDE eigenvalue problems involving parameter dependent matrices
Daniele Boffi, Francesca Gardini, Lucia Gastaldi
We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form $\m{A}x=λ\m{B}x$, where the matrices $\m{A…
The - and -versions of the virtual element method for elliptic eigenvalue problems
O. Certik, F. Gardini, G. Manzini +2
We discuss the - and the -versions of the virtual element method for the approximation of eigenpairs of elliptic operators with a potential term on polygonal meshes. An appl…
The virtual element method for eigenvalue problems with potential terms on polytopal meshes
Ondrej Certik, Francesca Gardini, Gianmarco Manzini +1
We extend the conforming virtual element method to the numerical resolution of eigenvalue problems with potential terms on a polytopal mesh. An important application is that of the…
The nonconforming virtual element method for eigenvalue problems
Francesca Gardini, Gianmarco Manzini, Giuseppe Vacca
We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the tw…
Virtual Element Method for Second Order Elliptic Eigenvalue Problems
Francesca Gardini, Giuseppe Vacca
We introduce the Virtual Element Method (VEM) for elliptic eigenvalue problems. The main result of the paper states that VEM provides an optimal order approximation of the eigenmod…
Optimal convergence of adaptive FEM for eigenvalue clusters in mixed form
Daniele Boffi, Dietmar Gallistl, Francesca Gardini +1
It is shown that the h-adaptive mixed finite element method for the discretization of eigenvalue clusters of the Laplace operator produces optimal convergence rates in terms of non…
A posteriori error analysis for nonconforming approximation of multiple eigenvalues
Daniele Boffi, Ricardo G. Durán, Francesca Gardini +1
In this paper we study an a posteriori error indicator introduced in E. Dari, R.G. Duran, C. Padra, Appl. Numer. Math., 2012, for the approximation of the Laplace eigenvalue proble…