Abstract
A system of linear coupled reaction-diffusion equations is considered, where each equation is a two-point boundary value problem and all equations share the same small diffusion coefficient. A finite element method using piecewise quadratic splines that are globally C 1 is introduced; its novelty lies in the norm associated with the method, which is stronger than the usual energy norm and is “balanced”, i.e., each term in the norm is O(1) when the norm is applied to the true solution of the system. On a standard Shishkin mesh with N subintervals, it is shown that the method is \(O(N^{-1}\ln N)\) accurate in the balanced norm. Numerical results to illustrate this result are presented.
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This paper was written while the first author was visiting the Beijing Computational Science Research Center, Haidian District, Beijing, China.
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Lin, R., Stynes, M. A balanced finite element method for a system of singularly perturbed reaction-diffusion two-point boundary value problems. Numer Algor 70, 691–707 (2015). https://doi.org/10.1007/s11075-015-9969-6
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DOI: https://doi.org/10.1007/s11075-015-9969-6