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Trefftz Methods and Taylor Series

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Abstract

The paper discusses Trefftz discretization techniques with a focus on their coupling with shape functions computed by the method of Taylor series. The paper highlights are, on one hand the control of ill-conditioning and the solving of large scale problems, on the other hand the applications to non-linear Partial Differential Equations. Indeed, despite excellent convergence properties, the practical use of Trefftz methods remains very limited because of their difficulty in treating nonlinearities and large systems.

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Acknowledgements

Michel Potier-Ferry thanks Pierre Ladevèze and Pierre Villon for helpful discussions about Trefftz and meshless methods.

Funding

This study was funded by National Research Agency ANR (Labex DAMAS, Grant No.ANR-11-LABX-0008-01).

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Authors and Affiliations

  1. School of Civil Engineering, Wuhan University, 8 South Road of East Lake, Wuchang, 430072, Wuhan, People’s Republic of China

    Jie Yang & Heng Hu

  2. Arts et Métiers ParisTech, Université de Lorraine, CNRS, LEM3, F-57000, Metz, France

    Michel Potier-Ferry, Koffi Akpama & Haitao Tian

  3. Luxembourg Institute of Science and Technology, 5, avenue des Hauts-Fourneaux, L-4362, Esch-sur-Alzette, Luxembourg

    Yao Koutsawa

  4. Laboratoire de Mathématiques-Informatique, Unité de Formation et de Recherche en Sciences Fondamentales et Appliquées, Université Nangui Abrogoua, 02 B.P. V 102, Abidjan, Côte d’Ivoire

    Djédjé Sylvain Zézé

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  1. Jie Yang
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Yang, J., Potier-Ferry, M., Akpama, K. et al. Trefftz Methods and Taylor Series. Arch Computat Methods Eng 27, 673–690 (2020). https://doi.org/10.1007/s11831-019-09330-2

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