Singularly perturbed reaction-diffusion equations in a circle with numerical applications
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- Singularly perturbed reaction-diffusion equations in a circle with numerical applications
- Jung, Chang-Yeol; Hong, Youngjoon; Laminie, Jacques
- asymptotic analysis; boundary layer; finite element method; reaction-diffusion equations; singular perturbations
- Issue Date
- TAYLOR & FRANCIS LTD
- INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, v.90, no.11, pp.2308 - 2325
- 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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