Burman, E;
Guzmán, J;
(2022)
Implicit-explicit multistep formulations for finite element discretisations using continuous interior penalty.
ESAIM: Mathematical Modelling and Numerical Analysis
, 56
(1)
pp. 349-383.
10.1051/m2an/2021084.
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Abstract
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 t2+hp+12 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. t≤Ch4/3. The theory is illustrated with some numerical examples.
| Type: | Article |
|---|---|
| Title: | Implicit-explicit multistep formulations for finite element discretisations using continuous interior penalty |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1051/m2an/2021084 |
| Publisher version: | https://doi.org/10.1051/m2an/2021084 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third-party material in this article are included in the Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10145159 |
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