Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.cma.2012.07.018
Title: Analysis of a new stabilized finite element method for the reaction-convection-diffusion equations with a large reaction coefficient
Authors: Duan, H.-Y.
Hsieh, P.-W.
Tan, R.C.E. 
Yang, S.-Y.
Keywords: Boundary layer
Finite element method
Interior layer
Reaction-convection-diffusion equation
Stabilization method
Issue Date: 1-Nov-2012
Citation: Duan, H.-Y., Hsieh, P.-W., Tan, R.C.E., Yang, S.-Y. (2012-11-01). Analysis of a new stabilized finite element method for the reaction-convection-diffusion equations with a large reaction coefficient. Computer Methods in Applied Mechanics and Engineering 247-248 : 15-36. ScholarBank@NUS Repository. https://doi.org/10.1016/j.cma.2012.07.018
Abstract: In this paper, we propose and analyze a new stabilized finite element method using continuous piecewise linear (or bilinear) elements for solving 2D reaction-convection-diffusion equations. The equation under consideration involves a small diffusivity ε and a large reaction coefficient σ, leading to high Péclet number and high Damköhler number. In addition to giving error estimates of the approximations in L 2 and H 1 norms, we explicitly establish the dependence of error bounds on the diffusivity, the L ∞ norm of convection field, the reaction coefficient and the mesh size. Our analysis shows that the proposed method is particularly suitable for problems with a small diffusivity and a large reaction coefficient, or more precisely, with a large mesh Péclet number and a large mesh Damköhler number. Several numerical examples exhibiting boundary or interior layers are given to illustrate the high accuracy and stability of the proposed method. The results obtained are also compared with those of existing stabilization methods. © 2012 Elsevier B.V.
Source Title: Computer Methods in Applied Mechanics and Engineering
URI: http://scholarbank.nus.edu.sg/handle/10635/102856
ISSN: 00457825
DOI: 10.1016/j.cma.2012.07.018
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