  In convection-dominated flows, robustness of the spatial discretisation is a
key property. While Interior Penalty Galerkin (IPG) methods already proved
efficient in the situation of large mesh Peclet numbers, Arbitrary
Lagrangian-Eulerian (ALE) methods are able to reduce the convection-dominance
by moving the mesh. In this paper, we introduce and analyse a velocity-based
moving mesh discontinuous Galerkin method for the solution of the linear
advection-diffusion equation. By introducing a smooth parameterized velocity
$\tilde{V}$ that separates the flow into a mean flow, also called moving mesh
velocity, and a remaining advection field $V-\tilde{V}$, we made a convergence
analysis based on the smoothness of the mesh velocity. Furthermore, the
reduction of the advection speed improves the stability of an explicit
time-stepping and the use of the nonconservative ALE formulation changes the
coercivity condition. Finally, by adapting the existing robust error criteria
to this moving mesh situation, we derived robust \textit{a posteriori} error
criteria that describe the potentially small deviation to the mean flow and
include the information of a transition towards $V=\tilde{V}$.
