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In this paper we present a Local Fourier Analysis of a space-time multigridsolver for a hyperbolic test problem. The space-time discretization is based onarbitrarily high order discontinuous Galerkin spectral element methods in timeand a first order finite volume method in space. We apply a block Jacobismoother and consider coarsening in space-time, as well as temporal coarseningonly. Asymptotic convergence factors for the smoother and the two-grid methodfor both coarsening strategies are presented. For high CFL numbers, theconvergence factors for both strategies are $0.5$ for first order, and $0.375$for second order accurate temporal approximations. Numerical experiments in oneand two spatial dimensions for space-time DG-SEM discretizations of varyingorder gives even better convergence rates of around $0.3$ and $0.25$ forsufficiently high CFL numbers.

Local Fourier Analysis of a Space-Time Multigrid Method for DG-SEM for the Linear Advection Equation