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2018 A Comparative Study on Stabilized Finite Element Methods for the Convection-Diffusion-Reaction Problems
Ali Sendur
J. Appl. Math. 2018: 1-16 (2018). DOI: 10.1155/2018/4259634


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.


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Ali Sendur. "A Comparative Study on Stabilized Finite Element Methods for the Convection-Diffusion-Reaction Problems." J. Appl. Math. 2018 1 - 16, 2018.


Received: 12 November 2017; Revised: 31 January 2018; Accepted: 14 February 2018; Published: 2018
First available in Project Euclid: 12 April 2018

zbMATH: 07132102
MathSciNet: MR3784080
Digital Object Identifier: 10.1155/2018/4259634

Rights: Copyright © 2018 Hindawi


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