Convergence Analysis of Finite Element Solution of One-Dimensional Singularly Perturbed Differential Equations on Equidistributing Meshes

Abstract

In this paper convergence on equidistributing meshes is investigated. Equidistributing meshes, or more generally approximate equidistributing meshes, are constructed through the well-known equidistribution principle and a so-called adaptation (or monitor) function which is defined based on estimates on interpolation error for polynomial preserving operators. Detailed convergence analysis is given for finite element solution of singularly perturbed two-point boundary value problems without turning points. Illustrative numerical results are given for a convection-diffusion problem and a reaction-diffusion problem.