Implicit a posteriori error estimation using patch recovery techniques

Tamás L. Horváth, F. Izsak

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    We develop implicit a posteriori error estimators for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedures. Convergence properties of the implicit error estimator are discussed independently of residual type error estimators, and this gives a freedom in the choice of boundary conditions. General assumptions are elaborated for the gradient averaging which define a family of implicit a posteriori error estimators. We will demonstrate the performance and the favor of the method through numerical experiments.
    Original languageUndefined
    Pages (from-to)55-72
    Number of pages18
    JournalCentral European journal of mathematics
    Issue number1
    Publication statusPublished - Jan 2012


    • MSC-65P99
    • MSC-70K70
    • MSC-70K99
    • EWI-21262
    • A posteriori error analysis
    • Gradient recovery
    • METIS-287845
    • IR-79471
    • Implicit methods

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