Trefftz methods are finite element-type schemes whose test and trial functions are (locally)
solutions of the targeted differential equation. They are particularly popular for time …

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 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 present and analyze a pollution-free Petrov–Galerkin multiscale finite element method
for the Helmholtz problem with large wave number κ as a variant of Peterseim (2014). We …

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 …

The application of computational modelling to wave propagation problems is hindered by
the dispersion error introduced by the discretisation. Two common strategies to address this …

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 …

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain
with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft …

We present and analyse a space–time discontinuous Galerkin method for wave propagation
problems. The special feature of the scheme is that it is a Trefftz method, namely that trial …

A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz
equation with piecewise constant coefficients. The construction of the corresponding local …