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) + epsilon(1/2N-k)) is proved, where k is the order of piecewise polynomials in the finite element method, eis the diffusion parameter and N is the number of partitions in each direction. Numerical experiments support this theoretical result. (C) 2020 Elsevier Inc. All rights reserved.