Embedded Trefftz discontinuous Galerkin methods

In Trefftz discontinuous Galerkin methods a partial differential equation is discretized using shape functions that are chosen to be elementwise in the kernel of corresponding operator. We propose new variant, embedded method, which projection an underlying method onto subspace Trefftz-type. The can described very general way and obtain it no have calculated explicitly, instead embedding operator constructed. simplest cases recovers established methods. But approach allows conveniently extend cases, including inhomogeneous sources non-constant coefficient operators. introduce discuss implementational aspects explore its potential on set standard PDE problems. Compared we observe severe reduction globally coupled unknowns all considered reducing computing time significantly. Moreover, for Helmholtz problem even improved accuracy similar based plane waves.