A posteriori error estimation for a defect-correction method applied to convection-diffusion problems
T. Linss 1, N. Kopteva 21 Institut fur Numerische Mathematik, Technische Universitat Dresden, D-01062 Dresden, Germany.
2 Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland.
Received by the editors September 1, 2009 and, in revised form, November 11, 2009.
We consider a two-point boundary-value problem for a singularly perturbed convection-diffusion problem. The problem is solved by using a defect-correction method based on a first-order upwind difference scheme and a second-order (unstabilized) central difference scheme. A robust a posteriori error estimate in the maximum norm is derived. It provides computable and guaranteed upper bounds for the discretization 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: Convection-diffusion problems, finite difference schemes, defect correction, a posteriori error estimation, singular perturbation.
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