Commuting Smoothed Projectors in Weighted Norms with an Application to Axisymmetric Maxwell Equations
This work was supported in part by the NSF under DMS-1014817
Journal of Scientific Computing
Finite element method, Interpolation, Algorithms
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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Published as: 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
This is the author’s version of a work that was accepted for publication in the Journal of Scientific Computing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. A definitive version was subsequently published in the Journal of Scientific Computing, (2012), Volume 51, Issue 2.