Barrenechea, GR;
Burman, E;
Karakatsani, F;
(2017)
Blending low-order stabilised finite element methods: A positivity-preserving local projection method for the convection–diffusion equation.
Computer Methods in Applied Mechanics and Engineering
, 317
pp. 1169-1193.
10.1016/j.cma.2017.01.016.
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Abstract
In this work we propose a nonlinear blending of two low-order stabilisation mechanisms for the convection–diffusion equation. The motivation for this approach is to preserve monotonicity without sacrificing accuracy for smooth solutions. The approach is to blend a first-order artificial diffusion method, which will be active only in the vicinity of layers and extrema, with an optimal order local projection stabilisation method that will be active on the smooth regions of the solution. We prove existence of discrete solutions, as well as convergence, under appropriate assumptions on the nonlinear terms, and on the exact solution. Numerical examples show that the discrete solution produced by this method remains within the bounds given by the continuous maximum principle, while the layers are not smeared significantly.
| Type: | Article |
|---|---|
| Title: | Blending low-order stabilised finite element methods: A positivity-preserving local projection method for the convection–diffusion equation |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.cma.2017.01.016 |
| Publisher version: | http://doi.org/10.1016/j.cma.2017.01.016 |
| Language: | English |
| Additional information: | Copyright © 2017 Elsevier Ltd. All rights reserved. This is an Open Access article made available under a Creative Commons Attribution Non-commercial Non-derivative 4.0 International license (CC BY-NC-ND 4.0). This license allows you to share, copy, distribute and transmit the work for personal and non-commercial use providing author and publisher attribution is clearly stated. Further details about CC BY licenses are available at http://creativecommons.org/ licenses/by/4.0. Access may be initially restricted by the publisher. |
| Keywords: | Discrete maximum principle; Convection–diffusion equation; Nonlinear scheme; Local projection stabilisation |
| 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/1546107 |
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