A Space-Time Trefftz Discontinuous Galerkin Method for the Linear Schrödinger Equation

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 space-time finite element method for the nonlinear Schröinger equation: the discontinuous Galerkin method

The convergence of the discontinuous Galerkin method for the nonlinear (cubic) Schrödinger equation is analyzed in this paper. We show the existence of the resulting approximations and prove optimal order error estimates in L∞(L2). These estimates are valid under weak restrictions on the space-time mesh.

A Space-time Finite Element Method for the Nonlinear Schrödinger Equation: the Discontinuous Galerkin Method

The convergence of the discontinuous Galerkin method for the nonlinear (cubic) Schrödinger equation is analyzed in this paper. We show the existence of the resulting approximations and prove optimal order error estimates in L∞(L2). These estimates are valid under weak restrictions on the space-time mesh.

Transparent boundary conditions for a discontinuous Galerkin Trefftz method

The modeling and simulation of electromagnetic wave propagation is often accompanied by a restriction to bounded domains which requires the introduction of artificial boundaries. The corresponding boundary conditions should be chosen in order to minimize parasitic reflections. In this paper, we investigate a new type of transparent boundary condition for a discontinuous Galerkin Trefftz finite ...

A Space-Time Discontinuous Galerkin Method for Extended Hydrodynamics