Bubble‐based stabilized finite element methods for time‐dependent convection–diffusion–reaction problems. (20th November 2016)

• Record Type: Journal Article
• Authors: Sendur, A.; Nesliturk, A.
• Is Part Of: International journal for numerical methods in fluids. Volume 82:Number 8(2016)
• Page Start: 512
• Page End: 538
• Publication Date: 2016-11-20
• Subjects: unsteady convection–diffusion–reaction problems -- stabilized finite element methods -- horizontal/vertical method of lines; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4229
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: In this paper, we propose a numerical algorithm for time‐dependent convection–diffusion–reaction problems and compare its performance with the well‐known numerical methods in the literature. Time discretization is performed by using fractional‐step θ ‐scheme, while an economical form of the residual‐free bubble method is used for the space discretization. We compare the proposed algorithm with the classical stabilized finite element methods over several benchmark problems for a wide range of problem configurations. The effect of the order in the sequence of discretization (in time and in space) to the quality of the approximation is also investigated. Numerical experiments show the improvement through the proposed algorithm over the classical methods in either cases. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : We present a numerical algorithm to get the approximate solution of time‐dependent convection–diffusion–reaction problems, especially in the case of small diffusion. The numerical method is based on fractional‐step θ ‐scheme in time combined with bubble‐based finite element methods in space. We further compare the proposed algorithm with two different stabilized methods on several benchmark problems. Numerical experiments illustrate the good performance of the proposed method even on coarse meshes as compared with the others.