Burman, E;
(2015)
A monotonicity preserving, nonlinear, finite element upwind method for the transport equation.
Applied Mathematics Letters
, 49
pp. 141-146.
10.1016/j.aml.2015.05.005.
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Abstract
We propose a simple upwind finite element method that is monotonicity preserving and weakly consistent of order O(h3/2). The scheme is nonlinear, but since an explicit time integration method is used the added cost due to the nonlinearity is not prohibitive. We prove the monotonicity preserving property for the forward Euler method and for a second order Runge–Kutta method. The convergence properties of the Runge–Kutta finite element method are verified on a numerical example.
| Type: | Article |
|---|---|
| Title: | A monotonicity preserving, nonlinear, finite element upwind method for the transport equation |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.aml.2015.05.005 |
| Publisher version: | http://dx.doi.org/10.1016/j.aml.2015.05.005 |
| Language: | English |
| Additional information: | © 2015. This manuscript version is published under a Creative Commons Attribution Non-commercial Non-derivative 4.0 International licence (CC BY-NC-ND 4.0). This licence 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 licences are available at http://creativecommons.org/licenses/by/4.0. |
| Keywords: | Stabilized finite element method; Shock capturing; Flux correction; Monotonicity preserving; Transport equation |
| 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/1476860 |
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