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IMA Journal of Numerical Analysis Advance Access originally published online on October 3, 2006
IMA Journal of Numerical Analysis 2007 27(3):576-592; doi:10.1093/imanum/drl020
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Maximum norm a posteriori error estimates for a 1D singularly perturbed semilinear reaction–diffusion problem

Natalia Kopteva{dagger}

Mathematics and Statistics Department, University of Limerick, Limerick, Ireland

{dagger} Email: natalia.kopteva{at}ul.ie

Received on 26 October 2005.


  Abstract

A singularly perturbed semilinear two-point boundary-value problem is discretized on arbitrary non-uniform meshes. We present second-order maximum norm a posteriori error estimates that hold true uniformly in the small parameter. Their application to monitor-function equidistribution and a posteriori mesh refinement are discussed. Numerical results are presented that support our theoretical estimates.

Key Words: reaction–diffusion; singular perturbation; finite differences; maximum norm; a posteriori error estimate; layer-adapted mesh; grid equidistribution


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