#### Title

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

#### Document Type

Article

#### Publication Title

Numerical Algorithms

#### 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 C1 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−1lnN)$O(N^{-1}\ln N)$ accurate in the balanced norm. Numerical results to illustrate this result are presented.

#### First Page

691

#### Last Page

707

#### DOI

10.1007/s11075-015-9969-6

#### Publication Date

12-1-2015

#### Recommended Citation

Lin, Runchang and Stynes, Martin, "A balanced finite element method for a system of singularly perturbed reaction-diffusion two-point boundary value problems" (2015). *Mathematics & Physics Faculty Publications*. 10.

https://rio.tamiu.edu/math_physics_facpubs/10