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 âˆ’Î”âˆ’ Ï‰2, Ï‰ > 0. They includeâ€¦ (More)

The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in the sense that the bilinear forms cannot be bounded below by a positive multiple of the appropriate normâ€¦ (More)

In this paper, we extend to the time-harmonic Maxwell equations the pâ€“version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for theâ€¦ (More)

The Ultra Weak Variational Formulation (UWVF) is a powerful numerical method for the approximation of acoustic, elastic and electromagnetic waves in the time-harmonic regime. The use of Trefftztypeâ€¦ (More)

This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory.â€¦ (More)

Trefftz methods are finite element-type schemes whose test a nd tri l functions are (locally) solutions of the targeted differential equation. They are particularly popular for time-harmonic waveâ€¦ (More)

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 obstacle. Ourâ€¦ (More)