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Jung, Chang-Yeol
Analysis and computational methods Lab
Research Interests
  • Analysis, singular perturbations, uncertainty, numerical methods

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Singularly perturbed reaction-diffusion equations in a circle with numerical applications

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Title
Singularly perturbed reaction-diffusion equations in a circle with numerical applications
Author
Jung, Chang-YeolHong, YoungjoonLaminie, Jacques
Keywords
asymptotic analysis; boundary layer; finite element method; reaction-diffusion equations; singular perturbations
Issue Date
201311
Publisher
TAYLOR & FRANCIS LTD
Citation
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, v.90, no.11, pp.2308 - 2325
Abstract
The goal of this article is to study the boundary layers of reaction-diffusion equations in a circle and provide some numerical applications which utilize the so-called boundary layer elements. Via the boundary layer analysis, we obtain the valid asymptotic expansions at any order and devise boundary layer elements to be conveniently used in the finite element schemes. Using boundary layer elements incorporated in the finite element space, we obtain accurate numerical solutions in a quasi-uniform mesh with convergence of order 2.
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DOI
http://dx.doi.org/10.1080/00207160.2013.772987
ISSN
0020-7160
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