Implicit-explicit multistep formulations for finite element discretisations using continuous interior penalty

We consider a finite element method with symmetric stabilisation for the discretisation of transient convection--diffusion equation. For time-discretisation we either second order backwards differentiation formula or Crank-Nicolson method. Both convection term and associated are treated explicitly using an extrapolated approximate solution. prove stability $\tau^2 + h^{p+{\frac12}}$ error estimates $L^2$-norm under standard hyperbolic CFL condition, when piecewise affine ($p=1$) approximation is used, in case $p \ge 1$, stronger, so-called $4/3$-CFL, i.e. $\tau \leq C h^{4/3}$. The theory illustrated some numerical examples.