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We introduce a new discretization based on the Trefftz-DG method for solvingthe Stokes equations. Discrete solutions of a corresponding method fulfill theStokes equation pointwise within each element and yield element-wisedivergence-free solutions. Compared to standard DG methods, a strong reductionof the degrees of freedom is achieved, especially for higher order polynomialdegrees. In addition, in contrast to many other Trefftz-DG methods, ourapproach allows to easily incorporate inhomogeneous right hand sides (drivingforces) by using the concept of the embedded Trefftz-DG method. On top of adetailed a priori error analysis, we further compare our approach to standarddiscontinuous Galerkin Stokes discretizations and present numerical examples.

Trefftz Discontinuous Galerkin discretization for the Stokes problem