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IMA Journal of Numerical Analysis 2001 21(1):107-122; doi:10.1093/imanum/21.1.107
© 2001 by Institute of Mathematics and its Applications
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The reliability of local error estimators for convection–diffusion equations

David Kay1 and David Silvester2

1 Centre for Mathematical Analysis and Its Applications, School of Mathematical Sciences, University of Sussex, Falmer, Brighton BN1 9QH, UK, e-mail: d.a.day{at}sussex.ac.uk 2 Department of Mathematics, UMIST, Manchester M60 1QD, UK, e-mail: na.silvester{at}na-net.ornl.gov

We assess the reliability of a simple a posteriori error estimator for steady-state convection–diffusion equations in cases where convection dominates. Our estimator is computed by solving a local Poisson problem with Neumann boundary conditions. It gives global upper and local lower bounds on the error measured in the H1 semi-norm. However, the error may be overestimated locally within boundary layers if these are not resolved by the mesh, that is, when the local mesh Péclet number is significantly greater than unity. We discuss the implications of this overestimation in a practical context where the estimator is used as a local error indicator within a self-adaptive mesh refinement process.

Received 18 June 1999. Accepted 7 March 2000.


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