主讲人：Klaus Böhmer 教授
单 位：德国马尔堡菲力普斯大学
题 目：A Convergence Theory for Mesh-free Methods for a Nonlinear Second Order Elliptic Equation
时 间：2013年10月22日上午 10:00 -- 11:30
地 点：理科楼-407
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.
报告人简介：德国马尔堡菲利普斯大学是世界上最古老的大学之一，创立于1527年。Klaus Böhmer 教授在偏微分方程领域是国际知名学者之一，他经常应邀在国际会议上报告，还多次组织国际会议或国际研讨会。他曾数次应邀来中国访问，进行交流与合作。
