Runge-Kutta multigrid analysis for space-time discontinuous Galerkin discretization of an advection-diffusion equation

In this article, we analyse the convergence of multigrid (MG) iteration for solving the algebraic equations arising from a space-time discontinuous Galerkin (DG) discretization of the advection-diffusion equation. To keep the MG method fully explicit, we consider Runge-Kutta smoothers that solve the algebraic equations by marching in pseudo-time to steady state. Depending on the