A balanced finite element method for a system of singularly perturbed reaction-diffusion two-point boundary value problems

作者：Lin Runchang; Stynes Martin^*

来源：Numerical Algorithms, 2015, 70(4): 691-707.

DOI：10.1007/s11075-015-9969-6

• Singular perturbation
• Reaction-diffusion
• Balanced norm
• Shishkin mesh
• Spline interpolant

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 piece-wise 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.

• 出版日期2015-12
• 单位北京计算科学研究中心