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SUMMARY:A nonlinear discretization theory  with applications to meshfree m
 ethods - Klaus Böhmer (University of Marburg)
DTSTART:20101028T140000Z
DTEND:20101028T150000Z
UID:TALK24109@talks.cam.ac.uk
CONTACT:6743
DESCRIPTION:We extend for the first time the linear discretization theory
  of Schaback\, developed for meshfree methods\, to nonlinear operator equa
 tions\, relying heavily on methods of B¨ohmer\, Vol I. There is no restri
 ction to elliptic problems or to symmetric numerical methods like Galerkin
  techniques. Trial spaces can be arbitrary\, but have to approximate the s
 olution well\, and testing can be weak or strong. We present Galerkin tech
 niques as an example. On the downside\, stability is not easy to prove for
  special applications\, and numerical methods have to be formulated as opt
 imization problems. Results of this discretization theory cover error boun
 ds and convergence rates. These results remain valid for the general case 
 of fully nonlinear elliptic differential equations of second order. Some 
 numerical examples are added for illustration. \n\nK. Böhmer\, Numerical 
 Methods for Nonlinear Elliptic Differential Equa\ntions\, Oxford Universi
 ty Press\, 2010\, 770 pp. \n\nR. Schaback\, Unsymmetric meshless methods f
 or operator equations\, Numer. Math.\, 114 (2010)\, pp. 629 - 651. \n
LOCATION:MR14\, CMS
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