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A second order nonconforming rectangular finite element method for approximating Maxwell’s equations

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Abstract

The main objective of this paper is to present a new rectangular nonconforming finite element scheme with the second order convergence behavior for approximation of Maxwell’s equations. Then the corresponding optimal error estimates are derived. The difficulty in construction of this finite element scheme is how to choose a compatible pair of degrees of freedom and shape function space so as to make the consistency error due to the nonconformity of the element being of order O(h 3), properly one order higher than that of its interpolation error O(h 2) in the broken energy norm, where h is the subdivision parameter tending to zero.

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Authors and Affiliations

  1. Department of Mathematics, Zhengzhou University, Zhengzhou, 450052, China

    Dong-yang Shi

  2. Department of Mathematical and Physical Sciences, Henan Institute of Engineering, Zhengzhou, 451191, China

    Xiao-bin Hao

Authors
  1. Dong-yang Shi
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  2. Xiao-bin Hao
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Corresponding author

Correspondence to Dong-yang Shi.

Additional information

Supported by the National Natural Science Foundation of China (No. 10971203), and the Doctor Foundation of Henan Institute of Engineering (No. D09008).

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Shi, Dy., Hao, Xb. A second order nonconforming rectangular finite element method for approximating Maxwell’s equations. Acta Math. Appl. Sin. Engl. Ser. 27, 739–748 (2011). https://doi.org/10.1007/s10255-011-0103-9

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  • DOI: https://doi.org/10.1007/s10255-011-0103-9

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