A negative-norm least-squares method for time-harmonic Maxwell equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:388

Article

Copeland, Dylan M.

关键词: Axisymmetry;    Least squares;    Maxwell equations;    Finite element;    Weighted Sobolev space;   

DOI  :  10.1016/j.jmaa.2011.09.004

来源: Elsevier

【 摘 要 】

This 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. (C) 2011 Elsevier Inc. All rights reserved.

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