Trefftz-DG discretization for the Stokes problem

Paul Stocker (Università di Vienna)

Abstract. We introduce a new discretization based on a polynomial Trefftz-DG method for solving the Stokes equations. Discrete solutions of this method fulfill the Stokes equations pointwise within each element and yield element-wise divergence-free solutions. Compared to standard DG methods, a strong reduction of the degrees of freedom is achieved, especially for higher polynomial degrees. In addition, in contrast to many other Trefftz-DG methods, our approach allows us to easily incorporate inhomogeneous right-hand sides (driving forces) by using the concept of the embedded Trefftz-DG method.