Adaptive finite element techniques for the Maxwell equations using implicit a posteriori error estimates

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

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    Abstract

    We consider an implicit a posteriori error estimation technique for the adaptive solution of the Maxwell equations with Nédélec edge finite element methods on three-dimensional domains. On each element of the tessellation an equation for the error is formulated and solved with a properly chosen local finite element basis. The discrete bilinear form of the local problems is shown to satisfy an inf–sup condition which ensures the well posedness of the error equations. An adaptive solution algorithm is developed based on the obtained error estimates. The performance of the method is tested on various problems including non-convex domains with non-smooth boundaries. The numerical results show that the estimated error, computed by the implicit a posteriori error estimation technique, correlates well with the actual error. On the meshes generated adaptively with the help of the error estimator, the achieved accuracy is higher than on globally refined meshes with comparable number degrees of freedom. Moreover, the rate of the error convergence on the locally adapted meshes is faster than that on the globally refined meshes.
    Original languageUndefined
    Article number10.1016/j.cma.2007.12.006
    Pages (from-to)1620-1638
    Number of pages19
    JournalComputer methods in applied mechanics and engineering
    Volume197
    Issue number17-18
    DOIs
    Publication statusPublished - Mar 2008

    Keywords

    • EWI-12005
    • MSC-74S05
    • MSC-65N15
    • IR-62193
    • MSC-65N50
    • METIS-250884
    • MSC-65N30

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