Barrenechea, GR;
Burman, E;
Karakatsani, F;
(2016)
Edge-based nonlinear diffusion for finite element approximations of convection - diffusion equations and its relation to algebraic flux-correction schemes.
Numerische Mathematik
, 135
(2)
pp. 521-545.
10.1007/s00211-016-0808-z.
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Barrenechea et al 2016 Edge-based nonlinear diffusion for finite element approximations of convection diffusion equations and its relation to algebraic flux-correction schemes VoR.pdf Download (906kB) | Preview |
Abstract
For the case of approximation of convection–diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The diffusion operator is shown to be Lipschitz continuous and linearity preserving. Using these properties we provide a full stability and error analysis, which, in the diffusion dominated regime, shows existence, uniqueness and optimal convergence. Then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters. The performance of the method is illustrated on some numerical test cases in two space dimensions.
| Type: | Article |
|---|---|
| Title: | Edge-based nonlinear diffusion for finite element approximations of convection - diffusion equations and its relation to algebraic flux-correction schemes |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00211-016-0808-z |
| Publisher version: | http://dx.doi.org/10.1007/s00211-016-0808-z |
| Language: | English |
| Additional information: | Copyright © The Author(s) 2016. Open Access: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS 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 |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1485730 |
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