Related papers: A virtual element approximation for the modified t…
In this paper, we analyze a virtual element method (VEM) for solving a non-selfadjoint fourth-order eigenvalue problem derived from the transmission eigenvalue problem. We write a variational formulation and propose a $C^1$-conforming…
The transmission eigenvalue problem is an important and challenging topic arising in the inverse scattering theory. In this paper, for the Helmholtz transmission eigenvalue problem, we give a weak formulation which is a nonselfadjoint…
We analyze in this paper a virtual element approximation for the acoustic vibration problem. We consider a variational formulation relying only on the fluid displacement and propose a discretization by means of H(div) virtual elements with…
We discuss the approximation of eigenvalue problems associated with elliptic partial differential equations using the virtual element method. After recalling the abstract theory, we present a model problem, describing in detail the features…
In this paper we analyze a conforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. We consider the classic velocity-pressure formulation which allows us to…
In this paper we analyze a nonconforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. The spaces under consideration lead to a divergence-free method which is…
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 two- and three-dimensional case.We present two possible…
Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse…
We introduce non conforming virtual elements to approximate the eigenvalues and eigenfunctions of the two dimensional acoustic vibration problem. We focus our attention on the pressure formulation of the acoustic vibration problem in order…
The transmission eigenvalue problem arises from the inverse scattering theory for inhomogeneous media and has important applications in many qualitative methods. The problem is posted as a system of two second order partial differential…
The goal of this paper is to develop numerical methods computing a few smallest elastic interior transmission eigenvalues, which are of practical importance in inverse elastic scattering theory. The problem is challenging since it is…
A recent problem of interest in inverse problems has been the study of eigenvalue problems arising from scattering theory and their potential use as target signatures in nondestructive testing of materials. Towards this pursuit we introduce…
This article presents a priori error estimates of the miscible displacement of one incompressible fluid by another through a porous medium characterized by a coupled system of nonlinear elliptic and parabolic equations. The study utilizes…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
A discrete analog is considered for the inverse transmission eigenvalue problem, having applications in acoustics. We provide a well-posed inverse problem statement, develop a constructive procedure for solving this problem, prove…
This article presents a priori error estimates of the miscible displacement of one compressible fluid by another in a porous medium. The study utilizes the $H(\rm div)$ conforming virtual element method (VEM) for the approximation of the…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method exactly conserves the system energy. To integrate in time…
We develop and analyse residual-based a posteriori error estimates for the virtual element discretisation of a nonlinear stress-assisted diffusion problem in two and three dimensions. The model problem involves a two-way coupling between…
In this paper we propose and analyze a virtual element method for the two dimensional non-symmetric diffusion-convection eigenvalue problem in order to derive a priori and a posteriori error estimates. Under the classic assumptions of the…