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

Burman, Erik; Guzmán, Johnny

doi:10.1051/m2an/2021084

Burman, Erik ; Guzmán, Johnny

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 1, pp. 349-383

Résumé

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 τ² + h$$ error estimates for the L²-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 ≤ Ch^4/3. The theory is illustrated with some numerical examples.

MR Zbl

DOI : 10.1051/m2an/2021084

Classification : 65M60
Keywords: IMEX – multistep, continuous interior penalty

@article{M2AN_2022__56_1_349_0,
     author = {Burman, Erik and Guzm\'an, Johnny},
     title = {Implicit-explicit multistep formulations for finite element discretisations using continuous interior penalty},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {349--383},
     year = {2022},
     publisher = {EDP-Sciences},
     volume = {56},
     number = {1},
     doi = {10.1051/m2an/2021084},
     mrnumber = {4379609},
     zbl = {1537.65125},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/m2an/2021084/}
}

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Burman, Erik; Guzmán, Johnny. Implicit-explicit multistep formulations for finite element discretisations using continuous interior penalty. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 1, pp. 349-383. doi: 10.1051/m2an/2021084

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