It is well‐known that when the geometry and/or coefficients allow stable trapped rays, the
outgoing solution operator of the Helmholtz equation grows exponentially through a …

We consider approximating the solution of the Helmholtz exterior Dirichlet problem for a
nontrapping obstacle, with boundary data coming from plane-wave incidence, by the …

In this paper, we investigate a posteriori error estimates of the Galerkin spectral methods for
second-order equations, and propose a simple type of error estimator comprising expansion …

We propose a novel a posteriori error estimator for conforming finite element discretizations
of two-and three-dimensional Helmholtz problems. The estimator is based on an …

We consider residual-based a posteriori error estimators for Galerkin discretizations of time-
harmonic Maxwell's equations. We focus on configurations where the frequency is high, or …

We consider interior penalty discontinuous Galerkin discretizations of time-harmonic wave
propagation problems modeled by the Helmholtz equation, and derive novel a priori and a …

We introduce several spatially adaptive model order reduction approaches tailored to non-
coercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz …

A posteriori upper and lower bounds are derived for the linear finite element method (FEM)
for the Helmholtz equation with large wavenumber. It is proved rigorously that the standard …

This paper presents an hp a posteriori error analysis for the 2D Helmholtz equation that is
robust in the polynomial degree p and the wave number k. For the discretization, we …

We consider time-harmonic Maxwell's equations set in a heterogeneous medium with
perfectly conducting boundary conditions. Given a divergence-free right-hand side lying in L …