The Mathematical Institute, University of Oxford, Eprints Archive

The reliability of local error estimators for convection-diffusion equations

Kay, David and Silvester, David (2000) The reliability of local error estimators for convection-diffusion equations. Technical Report. Unspecified. (Submitted)



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 $H^1$ semi-norm, except that the error may be over-estimated 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 over-estimation in a practical context where the estimator is used as a local error indicator within a self-adaptive mesh refinement process.

This work was supported by EPSRC grants GR/K91262 and GR/L05617.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1251
Deposited By: Lotti Ekert
Deposited On:21 May 2011 16:07
Last Modified:29 May 2015 18:56

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