An overview of the extended/generalized finite element method (GEFM/XFEM) with
emphasis on methodological issues is presented. This method enables the accurate …

Over the last decade, Computer Aided Engineering (CAE) tools have become essential in
the assessment and optimization of the acoustic characteristics of products and processes …

We develop a stability and convergence theory for a class of highly indefinite elliptic
boundary value problems (bvps) by considering the Helmholtz equation at high …

A rigorous convergence theory for Galerkin methods for a model Helmholtz problem in
${\mathbb {R}}^{d} $, $ d\in\{1, 2, 3\} $ is presented. General conditions on the approximation …

Plane wave discontinuous Galerkin (PWDG) methods are a class of Trefftz-type methods for
the spatial discretization of boundary value problems for the Helmholtz operator -Δ-ω^2 …

We introduce and analyze a virtual element method (VEM) for the Helmholtz problem with
approximating spaces made of products of low order VEM functions and plane waves. We …

We are concerned with a finite element approximation for time-harmonic wave propagation
governed by the Helmholtz equation. The usually oscillatory behavior of solutions, along …

We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of
the Helmholtz equation with large wave number $\kappa $ in bounded domains in $\mathbb …

We review the stability properties of several discretizations of the Helmholtz equation at
large wavenumbers. For a model problem in a polygon, a complete k-explicit stability …

We study the properties of a novel discontinuous Petrov Galerkin (DPG) method for acoustic
wave propagation. The method yields Hermitian positive definite matrices and has good pre …