A posteriori error estimation for a singularly perturbed problem with two small parameters
T. Linss 11 Institut fur Numerische Mathematik, Technische Universitat Dresden, D-01062 Dresden, Germany.
Received by the editors May 26, 2009 and, in revised form, October 24, 2009.
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.AMS subject classifications: 65L10, 65L12
Key words: Reaction-convection-diffusion problems, finite element methods, a posteriori error estimation, singular perturbation