Convergence of a finite element method on a Bakhvalov-type mesh for singularly perturbed reaction–diffusion equation

摘要

A finite element method is applied on a Bakhvalov-type mesh to solve a singularly perturbed reaction–diffusion problem whose solution exhibits boundary layers. A uniform convergence order of O(N−(k+1)+ε1/2N−k) is proved, where k is the order of piecewise polynomials in the finite element method, ε is the diffusion parameter and N is the number of partitions in each direction. Numerical experiments support this theoretical result.