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德国 Klaus Bohmer 教授讲座通知


  应数学与计算科学学院邀请,德国 Klaus Bohmer 教授来校讲学,欢迎全校师生参加。具体安排如下:  
  讲座题目:A Nonlinear Discretization Theory with Applications to Meshfree Methods for (Fully) Nonlinear PDEs  
  讲座时间:2011年5月6日下午16:30—18:00   
  讲座地点:东区F电2教室
       (数学与计算科学学院)
附:
A Nonlinear Discretization Theory with Applications to Meshfree Methods for (Fully) Nonlinear PDEs
K.B¨ohmer
Philipps-Universit¨at Marburg
Fachbereich Mathematik und Informatik
Abstract
  For the first time, we generalize the linear discretization theory of Schaback to nonlinear operator equations, elying heavily on methods of B¨ohmer. 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. 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 and convergence rates. As an example we present the meshless method for quasilinear and fully nonlinear elliptic problems of order 2.K. B¨ohmer, Numerical Methods for Nonlinear Elliptic Dfferential Equations,Oxford University Press, 2010, 770pp.R. Schaback, Unsymmetric meshless methods for operator equations,Numer. Math., 114 (2010), pp. 629 - 651.


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