Loading...
Blending low-order stabilised finite element methods: a positivity preserving local projection method for the convection-diffusion equation
Barrenechea, Gabriel Burman, Erik Karakatsani, Fotini
Barrenechea, Gabriel
Burman, Erik
Karakatsani, Fotini
Advisors
Editors
Other Contributors
EPub Date
Publication Date
2017-01-20
Submitted Date
Collections
Files
Loading...
Main article
Adobe PDF, 1.23 MB
Other Titles
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.
Citation
Barrenechea, G. R., et. al. (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, 1169-1193. DOI: 10.1016/j.cma.2017.01.2016
Publisher
Elsevier
Journal
Computer Methods in Applied Mechanics and Engineering
Research Unit
DOI
10.1016/j.cma.2017.01.016
PubMed ID
PubMed Central ID
Type
Article
Language
en
Description
Series/Report no.
ISSN
0045-7825
EISSN
1879-2138