Comparison of Adaptive Meshes for a Singularly Perturbed Reaction–Diffusion Problem

Abstract

We consider a singular second-order boundary value problem. The differential problem is approximated by the Galerkin finite element scheme. The main goal is to compare the well known apriori Bakhvalov and Shishkin meshes with the adaptive mesh based on the aposteriori dual error estimators. Results of numerical experiments are presented.

Keywords:

• singularly perturbed boundary value problem
• Galerkin method
• adaptive meshes
• a posteriori error estimates
• Shishkin mesh
• Bakhvalov mesh

AMS Subject Classification:

• 65L10
• 65L12
• 65L50