A space–time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients

Trefftz methods are high-order Galerkin schemes in which all discrete functions elementwise solution of the PDE to be approximated. They viable only when is linear and its coefficients piecewise-constant. We introduce a “quasi-Trefftz” discontinuous (DG) method for discretisation acoustic wave equation with piecewise-smooth material parameters: approximate solutions. show that new enjoys same excellent approximation properties as classical one, prove stability convergence DG scheme. polynomial basis spaces describe simple algorithm compute them. The technique we propose inspired by generalised plane waves previously developed time-harmonic problems variable coefficients; it turns out case time-domain under consideration quasi-Trefftz approach allows functions.