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We describe and analyse a space-time Trefftz discontinuous Galerkin methodfor the wave equation. The method is defined for unstructured meshes whoseinternal faces need not be aligned to the space-time axes. We show that thescheme is well-posed and dissipative, and we prove a priori error bounds forgeneral Trefftz discrete spaces. A concrete discretisation can be obtainedusing piecewise polynomials that satisfy the wave equation elementwise.

Trefftz discontinuous Galerkin methods on unstructured meshes for the wave equation