Parameter uniform convergence of a finite element method for a singularly perturbed linear reaction diffusion system with discontinuous source terms

Abstract

A linear system of ’n’ second order ordinary differential equations of reaction-diffusion type with discontinuous source terms is considered. On a piecewise uniform Shishkin mesh, a numerical system is built that employs the finite element method. The numerical approximations obtained by this approach are proven to be effectively almost second order convergent.

Keywords

• singular perturbation problems, system of differential equations, reaction - diffusion equations, overlapping boundary and interior layers, finite element method, shishkin mesh, parameter - uniform convergence, discontinuous source terms