Trefftz Methods and Taylor Series

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.