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Inverted finite elements for div-curl systems in the whole space

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Abstract

We use inverted finite element method (IFEM) for computing three-dimensional vector potentials and for solving div-curl systems in the whole space \(\mathbb {R}^{3}\). IFEM is substantially different from the existing approaches since it is a non truncature method which preserves the unboundness of the domain. After developping the method, we analyze its convergence in term of weighted norms. We then give some three-dimensional numerical results which demonstrate the efficiency and the accuracy of the method and confirm its convergence.

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Acknowledgements

Dr. Nabil Kerdid gratefully acknowledges the support of the National Plan for Science, Technology and Information (Maarifah), King Abdulaziz City for Science and Technology, KSA, award number 12-MAT2996-08.

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Authors and Affiliations

  1. Laboratoire de Mathématiques de Versailles, Université de Versailles Saint-Quentin-en-Yvelines - Université Paris-Saclay 45, avenue des Etats-Unis, 78035, Versailles, Cedex, France

    Tahar Z. Boulmezaoud & Keltoum Kaliche

  2. Department of Mathematics and Statistics, Al Imam Bin Saud University, College of Sciences, PO-Box 90950, Riyadh, 11623, Kingdom of Saudi Arabia

    Nabil Kerdid

Authors
  1. Tahar Z. Boulmezaoud
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  2. Keltoum Kaliche
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  3. Nabil Kerdid
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Correspondence to Tahar Z. Boulmezaoud.

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Communicated by: Aihui Zhou

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Boulmezaoud, T.Z., Kaliche, K. & Kerdid, N. Inverted finite elements for div-curl systems in the whole space. Adv Comput Math 43, 1469–1489 (2017). https://doi.org/10.1007/s10444-017-9532-1

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  • DOI: https://doi.org/10.1007/s10444-017-9532-1

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