199 citations · 431 across the 51 of their papers we have counts for
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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…
DPG approximation of eigenvalue problems
Fleurianne Bertrand, Daniele Boffi, Henrik Schneider
In this paper, the discontinuous Petrov--Galerkin approximation of the Laplace eigenvalue problem is discussed. We consider in particular the primal and ultra weak formulations of…
On the existence and the uniqueness of the solution to a fluid-structure interaction problem
Daniele Boffi, Lucia Gastaldi
In this paper we consider the linearized version of a system of partial differential equations arising from a fluid-structure interaction model. We prove the existence and the uniq…
Convergence analysis of the scaled boundary finite element method for the Laplace equation
Fleurianne Bertrand, Daniele Boffi, Gonzalo G. de Diego
The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamenta…
An adaptive finite element scheme for the Hellinger--Reissner elasticity mixed eigenvalue problem
Fleurianne Bertrand, Daniele Boffi, Rui Ma
In this paper we study the approximation of eigenvalues arising from the mixed Hellinger--Reissner elasticity problem by using the simple finite element using partial relaxation of…
Convergence of Lagrange finite elements for the Maxwell Eigenvalue Problem in 2D
Daniele Boffi, Johnny Guzman, Michael Neilan
We consider finite element approximations of the Maxwell eigenvalue problem in two dimensions. We prove, in certain settings, convergence of the discrete eigenvalues using Lagrange…
Least-squares for linear elasticity eigenvalue problem
Fleurianne Bertrand, Daniele Boffi
We study the approximation of the spectrum of least-squares operators arising from linear elasticity. We consider a two-field (stress/displacement) and a three-field (stress/displa…
First order least-squares formulations for eigenvalue problems
Fleurianne Bertrand, Daniele Boffi
In this paper we discuss spectral properties of operators associated with the least-squares finite element approximation of elliptic partial differential equations. The convergence…
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…