摘  要：Numerical Methods for Nonlinear Elliptic Differential Equations, A Synopsis, 2010 and 2014:Numerical Methods for Bifurcation and Center Manifolds in Nonlinear Elliptic and Parabolic Differential Equations.

         We extend for the first time the linear discretization theory of Schaback, developed for meshfree methods, to nonlinear operator equations, relying heavily on methods of Bohmer, Vol I. There is no restriction to elliptic problems nor to symmetric numerical methods like Galerkin techniques. Trial spaces can be arbitrary, but have to approximate the solution well, and testing can be weak or strong. We present Galerkin techniques as an example. On the downside, stability is not easy to prove for special applications, and numerical methods have to be formulated as optimization problems. Results of this discretization theory cover error bounds, convergence rates of discrete solutions and Newton methods. As examples we present the meshless method for a simple nonlinear and a fully nonlinear elliptic problem of second order. Numerical examples are added for illustration.