A Comparative Study on Stabilized Finite Element Methods for the Convection-Diffusion-Reaction Problems
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-03-26
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
The disproportionality in the problem parameters of the convection-diffusion-reaction equation may lead to the formation of layer structures in some parts of the problem domain which are difficult to resolve by the standard numerical algorithms.
Therefore the use of a stabilized numerical method is inevitable.
In this work, we employ and compare three classical stabilized finite element formulations, namely, the Streamline-Upwind Petrov-Galerkin (SUPG), Galerkin/Least-Squares (GLS), and Subgrid Scale (SGS) methods, and a recent Link-Cutting Bubble (LCB) strategy proposed by Brezzi and his coworkers for the numerical solution of the convection-diffusion-reaction equation, especially in the case of small diffusion.
On the other hand, we also consider the pseudo residual-free bubble (PRFB) method as another alternative that is based on enlarging the finite element space by a set of appropriate enriching functions.
We compare the performances of these stabilized methods on several benchmark problems.
Numerical experiments show that the proposed methods are comparable and display good performance, especially in the convection-dominated regime.
However, as the problem turns into reaction-dominated case, the PRFB method is slightly better than the other well-known and extensively used stabilized finite element formulations as they start to exhibit oscillations.
American Psychological Association (APA)
Sendur, Ali. 2018. A Comparative Study on Stabilized Finite Element Methods for the Convection-Diffusion-Reaction Problems. Journal of Applied Mathematics،Vol. 2018, no. 2018, pp.1-16.
https://search.emarefa.net/detail/BIM-1176012
Modern Language Association (MLA)
Sendur, Ali. A Comparative Study on Stabilized Finite Element Methods for the Convection-Diffusion-Reaction Problems. Journal of Applied Mathematics No. 2018 (2018), pp.1-16.
https://search.emarefa.net/detail/BIM-1176012
American Medical Association (AMA)
Sendur, Ali. A Comparative Study on Stabilized Finite Element Methods for the Convection-Diffusion-Reaction Problems. Journal of Applied Mathematics. 2018. Vol. 2018, no. 2018, pp.1-16.
https://search.emarefa.net/detail/BIM-1176012
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1176012