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Hodge Decomposition Methods for a Quad-Curl Problem on Planar Domains

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Abstract

We develop and analyze \(P_k\) Lagrange finite element methods for a quad-curl problem on planar domains that is based on the Hodge decomposition of divergence-free vector fields. Numerical results that illustrate the performance of the finite element methods are also presented.

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Acknowledgements

The work of the first and third authors was supported in part by the National Science Foundation under Grant Nos. DMS-13-19172 and DMS-16-20273. The work of the second author was supported in part by the National Science Foundation under Grant No. DMS-15-21555.

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Authors and Affiliations

  1. Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, 70803, USA

    Susanne C. Brenner & Li-yeng Sung

  2. Department of Mathematics Sciences, Michigan Technological University, Houghton, MI, 49931, USA

    Jiguang Sun

Authors
  1. Susanne C. Brenner
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  2. Jiguang Sun
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  3. Li-yeng Sung
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Correspondence to Susanne C. Brenner.

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Brenner, S.C., Sun, J. & Sung, Ly. Hodge Decomposition Methods for a Quad-Curl Problem on Planar Domains. J Sci Comput 73, 495–513 (2017). https://doi.org/10.1007/s10915-017-0449-0

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  • DOI: https://doi.org/10.1007/s10915-017-0449-0

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