A space-time Trefftz discontinuous Galerkin method for the acoustic wave equation in first-order formulation (Q681701)

A space-time Trefftz discontinuous Galerkin method is analyzed for the solution of the acoustic wave equation in the first-order formulation in arbitrary space dimensions. The key feature of the discrete scheme is that the test and trial discrete functions are space-time piecewise polynomial solutions of the wave equation. The authors prove various results regarding the well-posedness and a priori error bounds in skeleton-based and mesh independent norms. A detailed description of two appropriate Trefftz spaces is also provided. It is an interesting paper.