Abstract: Numerical Analysis of PDEs relies on the creation and the study of a numerical scheme. Numerical analysists distinguishe two different types of error for numerical scheme. The consistency error is the difference between the exact solution of the differential equation and the solution of the numerical scheme. The numerical stability of a numerical scheme consists in describing the propagation of the computing error for iterative methods. This talk aimed to show that these two notions are useful for linear PDEs but fail to apprehend numerical analysis for nonlinear PDEs. In order to highlight different stakes in numerical simulation, this talk will present some usual numerical methods and introduce an innovative type of numerical methods called “meshless”.