We discuss the stability theory and numerical analysis of the Helmholtz equation with
variable and possibly nonsmooth or oscillatory coefficients. Using the unique continuation …

We consider the Helmholtz transmission problem with one penetrable star-shaped Lipschitz
obstacle. Under a natural assumption about the ratio of the wavenumbers, we prove bounds …

A convergence theory for the hp-FEM applied to a variety of constant-coefficient Helmholtz
problems was pioneered in the papers [35],[36],[15],[34]. This theory shows that, if the …

We analyse the convergence of finite element discretizations of time-harmonic wave
propagation problems. We propose a general methodology to derive stability conditions and …

We introduce a novel multi-resolution localized orthogonal decomposition (LOD) for time-
harmonic acoustic scattering problems that can be modeled by the Helmholtz equation. The …

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 study the resolvent for nontrapping obstacles on manifolds with Euclidean ends. It is well
known that for such manifolds the outgoing resolvent satisfies∥ χ R (k) χ∥ L 2→ L 2≤ C k …

We propose a novel variant of the Localized Orthogonal Decomposition (LOD) method for
time-harmonic scattering problems of Helmholtz type with high wavenumber. On a coarse …

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 the analysis of the-version of the finite-element method (FEM), with fixed polynomial
degree, applied to the Helmholtz equation with wavenumber, the asymptotic regime is when …