A negative-norm least-squares method for time-harmonic Maxwell equations
AuthorsCopeland, Dylan M.
KAUST Grant NumberKUS-C1-016-04
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AbstractThis paper presents and analyzes a negative-norm least-squares finite element discretization method for the dimension-reduced time-harmonic Maxwell equations in the case of axial symmetry. The reduced equations are expressed in cylindrical coordinates, and the analysis consequently involves weighted Sobolev spaces based on the degenerate radial weighting. The main theoretical results established in this work include existence and uniqueness of the continuous and discrete formulations and error estimates for simple finite element functions. Numerical experiments confirm the error estimates and efficiency of the method for piecewise constant coefficients. © 2011 Elsevier Inc.
CitationCopeland DM (2012) A negative-norm least-squares method for time-harmonic Maxwell equations. Journal of Mathematical Analysis and Applications 388: 303–317. Available: http://dx.doi.org/10.1016/j.jmaa.2011.09.004.
SponsorsThe author thanks Prof. Joseph E. Pasciak for helpful discussions in developing the theory for this work. This publication is based on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).