Meshless and generalized FEM
               Some theoretical results and applications

                             Ivo Babuska

       The Institute for Computational Engineering and Sciences
                    University of Texas at Austin

                               Abstract

  There are about 250,000 papers on classical FEM and its applications.
In contrast only about 250 papers on Meshless and Generalized FEM were
published. Essentially all were published in engineering journals in
last few years.
  The talk will present the main ideas of  Meshless and Generalized FEM
and focus on the differences with the classical FEM. Here for example
the meshes are not used and the shape functions do not need to be
polynomial which allows to solve PDEs with microstructure etc.
Illustrative theoretical and computational results will be presented.