The reliability of local error estimators for convection-diffusion equations

David Kay, David Silvester

    Research output: Contribution to journalArticlepeer-review


    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.
    Original languageEnglish
    Pages (from-to)107-122
    Number of pages15
    JournalIMA Journal of Numerical Analysis
    Issue number1
    Publication statusPublished - Jan 2001


    Dive into the research topics of 'The reliability of local error estimators for convection-diffusion equations'. Together they form a unique fingerprint.

    Cite this