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A curl-conforming weak Galerkin method for the quad-curl problem

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Abstract

The quad-curl problem arises from the inverse electromagnetic scattering theory and magnetohydrodynamics. In this paper, a weak Galerkin method is proposed using the curl-conforming Nédélec elements. On one hand, the method avoids the construction of the curl–curl conforming elements and thus solves a smaller linear system. On the other hand, it is much simpler than the case of using the fully discontinuous elements. For polynomial spaces of order k, error estimates of \(O(h^{k-1})\) in the energy norm and of \(O(h^{k})\) in the \(H(\text {curl})\) norm are established, which are validated by the numerical examples.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, 49931, USA

    Jiguang Sun

  2. Beijing Computational Science Research Center, Beijing, 100193, China

    Qian Zhang & Zhimin Zhang

  3. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    Zhimin Zhang

Authors
  1. Jiguang Sun
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  2. Qian Zhang
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  3. Zhimin Zhang
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Correspondence to Qian Zhang.

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Communicated by Ragnar Winther.

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This research was supported in part by the National Natural Science Foundation of China under Grants NSFC 11471031, NSFC 91430216, NSAF U1530401, and the US National Science Foundation under Grants DMS-1419040 and DMS-1521555.

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Sun, J., Zhang, Q. & Zhang, Z. A curl-conforming weak Galerkin method for the quad-curl problem. Bit Numer Math 59, 1093–1114 (2019). https://doi.org/10.1007/s10543-019-00764-5

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