A Space-Time Discontinuous Galerkin Trefftz Method for Time Dependent Maxwell's Equations

A Trefftz Polynomial Space-Time Discontinuous Galerkin Method for the Second Order Wave Equation

A new space-time discontinuous Galerkin (dG) method utilizing special Trefftz polynomial basis functions is proposed and fully analyzed for the scalar wave equation in a second order formulation. The dG method considered is motivated by the class of interior penalty dG methods, as well as by the classical work of Hughes and Hulbert [Comput. Methods Appl. Mech. Engrg., 66 (1988), pp. 339–363; Co...

A hybridizable discontinuous Galerkin method for time-harmonic Maxwell’s equations

In this paper, we study a bybridizable discontinuous Galerkin (HDG) method for the numerical solution of 2D time-harmonic Maxwell’s equations. The formulations are given, and the relationship between the HDG scheme and the upwind flux DG method is also examined. The presented numerical results show the effectiveness of the proposed HDG method especially in comparison to the upwind flux DG metho...

A Space-Time Discontinuous Galerkin Method for Extended Hydrodynamics

Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations

In this paper, we extend to the time-harmonic Maxwell equations the p–version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version, SIAM J. Numer. Anal., 49 (2011), 264-284] for Trefftz-discontinuous Galerkin approximations of the Helmholtz problem. While error estimates in a me...

Space - time discontinuous Galerkin method for compressible flow

titled Advanced simulation techniques for vortex dominated flows in aerodynamics. The financial support from STW and the National Aerospace Laboratory NLR is gratefully acknowledged.