Trefftz Methods and Taylor Series
J. Yang, M. Potier-Ferry, K. Akpama, H. Hu, Y. Koutsawa, H.T. Tian, and D.S. Zeze
Archives of Computational Methods in Engineering, vol. 27, no. 3, p. 673-690, 2020
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.