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BIT Numerical Mathematics

, Volume 59, Issue 4, pp 1093–1114 | Cite as

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

  • Jiguang Sun
  • Qian ZhangEmail author
  • Zhimin Zhang
Article
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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.

Keywords

Quad-curl problem WG methods Edge elements 

Mathematics Subject Classification

65N30 35Q60 65N15 35B45 
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Notes

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesMichigan Technological UniversityHoughtonUSA
  2. 2.Beijing Computational Science Research CenterBeijingChina
  3. 3.Department of MathematicsWayne State UniversityDetroitUSA

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