Abstract
We construct finite element projectors that can be applied to functions with low regularity. These projectors are continuous in a weighted norm arising naturally when modeling devices with axial symmetry. They have important commuting diagram properties needed for finite element analysis. As an application, we use the projectors to prove quasioptimal convergence for the edge finite element approximation of the axisymmetric time-harmonic Maxwell equations on nonsmooth domains. Supplementary numerical investigations on convergence deterioration at high wavenumbers and near Maxwell eigenvalues and are also reported.
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This work was supported in part by the NSF under DMS-1014817. The authors also gratefully acknowledge the support from the IMA (Minneapolis) during their 2010-11 annual program.
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Gopalakrishnan, J., Oh, M. Commuting Smoothed Projectors in Weighted Norms with an Application to Axisymmetric Maxwell Equations. J Sci Comput 51, 394–420 (2012). https://doi.org/10.1007/s10915-011-9513-3
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DOI: https://doi.org/10.1007/s10915-011-9513-3