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A nonconforming finite element method for a two-dimensional curl–curl and grad-div problem

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Abstract

A numerical method for a two-dimensional curl–curl and grad-div problem is studied in this paper. It is based on a discretization using weakly continuous P 1 vector fields and includes two consistency terms involving the jumps of the vector fields across element boundaries. Optimal convergence rates (up to an arbitrary positive \({\epsilon}\)) in both the energy norm and the L 2 norm are established on graded meshes. The theoretical results are confirmed by numerical experiments.

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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

    S. C. Brenner

  2. Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803, USA

    J. Cui & L.-Y. Sung

  3. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    F. Li

Authors
  1. S. C. Brenner
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  2. J. Cui
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  3. F. Li
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  4. L.-Y. Sung
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Corresponding author

Correspondence to S. C. Brenner.

Additional information

The work of the first author was supported in part by the National Science Foundation under Grant No. DMS-03-11790 and by the Humboldt Foundation through her Humboldt Research Award. The work of the third author was supported in part by the National Science Foundation under Grant No. DMS-06-52481.

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Brenner, S.C., Cui, J., Li, F. et al. A nonconforming finite element method for a two-dimensional curl–curl and grad-div problem. Numer. Math. 109, 509–533 (2008). https://doi.org/10.1007/s00211-008-0149-7

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  • DOI: https://doi.org/10.1007/s00211-008-0149-7

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