A Posteriori Error Estimation for a Singularly Perturbed Problem with Two Small Parameters

Abstract

A singularly perturbed two-point boundary-value problem of reaction-convection-diffusion type is considered. The problem involves two small parameters that give rise to two boundary layers of different widths. The problem is solved using a streamline-diffusion FEM (SDFEM).
A robust a posteriori error estimate in the maximum norm is derived. It provides computable and guaranteed upper bounds for the discretisation error.
Numerical examples are given that illustrate the theoretical findings and verify the efficiency of the error estimator on a priori adapted meshes and in an adaptive mesh movement algorithm.