Minerva  

19th GAMM-Seminar Leipzig on
High-dimensional problems - Numerical treatment and applications

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
Phone: +49.341.9959.752, Fax: +49.341.9959.999


     
  Homepage  
     
  19th GAMM-Seminar
January, 23th-25th, 2003
 
     
  Announcement  
  Registration  
  Participants  
  Programme  
  Abstracts ->
  Proceedings  
     
  Archive  
     
  All seminars  
  All proceedings  
     
 
  Abstract Andrej Nitsche, Fri, 11.00-11.25 Previous Contents Next  
  Sparse approximation of singularity functions
Andrej Nitsche (ETH Zürich)

We are concerned with the sparse approximation of functions of type
displaymath14
on the d-dimensional unit cube tex2html_wrap_inline20 with parameters tex2html_wrap_inline22, tex2html_wrap_inline24, smooth g, a smooth cut-off function tex2html_wrap_inline28, and a function tex2html_wrap_inline30 of the remaining coordinates but |x|, possibly singular as well (e. g. containing edge singularities). These functions arise e. g. from corners of domains in solutions to elliptic PDEs. Usually, they deteriorate the rate of convergence of numerical algorithms to approximate these solutions.
We show, that functions of this type - for a range of tex2html_wrap_inline34 covering elliptic singularities - can be approximated with respect to the tex2html_wrap_inline36 norm by sparse grid wavelet spaces tex2html_wrap_inline38, tex2html_wrap_inline40, of biorthogonal spline wavelets of degree p essentially at the rate p:
displaymath15
where tex2html_wrap_inline46 is a weighted Sobolev norm and tex2html_wrap_inline48.
 

 
    Previous Contents Next  


Last updated:
30.11.2004 Impressum
 
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
Valid HTML 4.0!