Implicit a posteriori error estimates for the Maxwell equations

F. Izsak, D. Harutyunyan, Jacobus J.W. van der Vegt

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    An implicit a posteriori error estimation technique is presented and analyzed for the numerical solution of the time-harmonic Maxwell equations using Nédélec edge elements. For this purpose we define a weak formulation for the error on each element and provide an efficient and accurate numerical solution technique to solve the error equations locally. We investigate the well-posedness of the error equations and also consider the related eigenvalue problem for cubic elements. Numerical results for both smooth and non-smooth problems, including a problem with reentrant corners, show that an accurate prediction is obtained for the local error, and in particular the error distribution, which provides essential information to control an adaptation process. The error estimation technique is also compared with existing methods and provides significantly sharper estimates for a number of reported test cases.
    Original languageUndefined
    Article number10.1090/S0025-5718-08-02046-2
    Pages (from-to)1355-1386
    Number of pages32
    JournalMathematics of computation
    Issue numberWP 08-02/263
    Publication statusPublished - 20 Feb 2008


    • MSC-65N15
    • MSC-65N30
    • MSC-65R20
    • Maxwell equations
    • IR-65317
    • Nédélec edge finite elements.
    • implicit estimates
    • EWI-14913
    • METIS-255136
    • a posteriori error estimates

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