File(s) not publicly available
Time-stepping schemes for moving grid finite elements applied to reaction-diffusion systems on fixed and growing domains
journal contribution
posted on 2023-06-08, 07:30 authored by Anotida MadzvamuseIn this paper, we illustrate the application of time-stepping schemes to reaction-diffusion systems on fixed and continuously growing domains by use of finite element and moving grid finite element methods. We present two schemes for our studies, namely a first-order backward Euler finite differentiation formula coupled with a special form of linearisation of the nonlinear reaction terms (1-SBEM) and a second-order semi-implicit backward finite differentiation formula (2-SBDF) with no linearisation of the reaction terms. Our results conclude that for the type of reaction-diffusion systems considered in this paper, the 1-SBEM is more stable than the 2-SBDF scheme and that the 1-SBEM scheme has a larger region of stability (at least by a factor of 10) than that of the 2-SBDF scheme. As a result, the 1-SBEM scheme becomes a natural choice when solving reaction-diffusion problems on continuously deforming domains.
History
Publication status
- Published
Journal
Journal of Computational PhysicsISSN
0021-9991Publisher
ElsevierExternal DOI
Issue
1Volume
214Page range
239 - 263Pages
25.0Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC