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18th GAMM-Seminar Leipzig on
Multigrid and related methods for optimization problems

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
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  18th GAMM-Seminar
January, 24th-26th, 2002
 
     
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  Abstract Petr Knobloch, Fri, 15.00-15.25 Previous Contents Next  
  General convergence analysis of non-nested multi-level solvers for FE discretizations of mixed problems
Petr Knobloch (Charles University Praha)

We investigate the convergence of multi-level solvers for finite element discretizations of an abstract mixed problem. As a basic new feature, our approach allows to use different finite element discretizations on each level of the multi-grid hierarchy. Typically, one uses different finite element spaces, which may be both conforming and nonconforming, but the use of different bilinear forms is also allowed. Thus, several levels of the multi-level algorithm may correspond to one geometrical grid (i.e., to one triangulation). Particularly, our theory enables to combine accurate higher order finite element discretizations on the finest level with low order finite element discretizations on all other levels. In this way, an accurate solution can be obtained for whose computation the efficiency of multi--level solvers for low order discretizations is exploited. That leads to the design of efficient multi-level solvers for higher order finite element discretizations. This is a joint work with Volker John, Gunar Matthies and Lutz Tobiska from the University of Magdeburg.
 

 
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