A comparative study on stabilized finite element methods for the convection-diffusion-reaction problems
type: Item
instance of: scholarly article
title: A comparative study on stabilized finite element methods for the convection-diffusion-reaction problems
zbMATH Open document ID: 1437.65199
DOI: 10.1155/2018/4259634
author: Ali Sendur
published in: Journal of Applied Mathematics
publication date: 2019-11-19T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 7132102
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/4259634
OpenAlex ID: W2789960349
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Wikidata QID: Q130065521
description: scientific article