Related papers: Finite element eigenvalue enclosures for the Maxwe…

This study proposes a class of augmented subspace schemes for the weak Galerkin (WG) finite element method used to solve eigenvalue problems. The augmented subspace is built with the conforming linear finite element space defined on the…

We study the high-frequency behavior of the Dirichlet-to-Neumann map for an arbitrary compact Riemannian manifold with a non-empty smooth boundary. We show that far from the real axis it can be approximated by a simpler operator. We use…

We study resonance for the Helmholz equation with a finite frequency in a plasmonic material of negative dielectric constant in two and three dimensions. We show that the quasi-static approximation is valid for diametrically small…

Motivated by applications to numerical simulation of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the…

We propose and analyze a finite element method for the Oseen eigenvalue problem. This problem is an extension of the Stokes eigenvalue problem, where the presence of the convective term leads to a non-symmetric problem and hence, to complex…

In this paper we propose and analyze a virtual element method to approximate the natural frequencies of the acoustic eigenvalue problem with polygonal meshes that allow the presence of small edges. With the aid of a suitable seminorm that…

The aim of the paper is to introduce a new systematic method that can produce lower bounds for eigenvalues. The main idea is to use nonconforming finite element methods. The general conclusion herein is that if local approximation…

We present a novel integral-equation algorithm for evaluation of Zaremba eigenvalues and eigenfunctions}, that is, eigenvalues and eigenfunctions of the Laplace operator with mixed Dirichlet-Neumann boundary conditions; of course, (slight…

Numerical methods for the transmission eigenvalue problems are hot topics in recent years. Based on the work of Lin and Xie [Math. Comp., 84(2015), pp. 71-88], we build a multigrid method to solve the problems. With our method, we only need…

This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…

Recent advancements in finite element methods allows for the implementation of mesh cells with curved edges. In the present work, we develop the tools necessary to employ multiply connected mesh cells, i.e. cells with holes, in planar…

We propose and analyze an augmented mixed finite element method for the pseudostress-velocity formulation of the stationary convective Brinkman-Forchheimer problem in $\mathrm{R}^d$, $d\in \{2,3\}$. Since the convective and Forchheimer…

We consider a coefficient inverse problem for the dielectric permittivity in Maxwell's equations, with data consisting of boundary measurements of one or two backscattered or transmitted waves. The problem is treated using a Lagrangian…

We study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl's analysis…

This paper presents an asymptotically compatible error bound for the finite element method (FEM) applied to a nonlocal diffusion model. The analysis covers two scenarios: meshes with and without shape regularity. For shape-regular meshes,…

We consider a large-scale quadratic eigenvalue problem (QEP), formulated using P1 finite elements on a fine scale reference mesh. This model describes damped vibrations in a structural mechanical system. In particular we focus on problems…

Scattering resonances have important applications in many areas of science and engineering. They are the replacement of discrete spectral data for problems on non-compact domains. In this paper, we consider the computation of scattering…

This paper studies the nonconforming Morley finite element approximation of the eigenvalues of the biharmonic operator. A new $C^1$ conforming companion operator leads to an $L^2$ error estimate for the Morley finite element method which…

Magnetostatic field calculations in micromagnetic simulations can be numerically expensive, particularly in the case of large-scale finite element simulations. The established finite element / boundary element method (FEM/BEM) by Fredkin &…

We present an easy-to-implement numerical method for analyzing electromagnetic wave propagation in dielectric rings. Our approach employs a finite-difference-based solver in cylindrical coordinates, solving a mixed electric-magnetic field…