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