Non-nested Multi-level Solvers for Finite Element Discretizations of Mixed Problems

V. John
Institut f¨r Analysis und Numerik
Otto-von-Guericke-Universit at Magdeburg, PF 4120
D-39016 Magdeburg, Germany

P. Knobloch
Institute of Numerical Mathematics
Faculty of Mathematics and Physics
Charles University
Sokolovsk a 83, 186 75 Praha 8, Czech Republic

G. Matthies and L. Tobiska
Institut f¨r Analysis und Numerik
Otto-von-Guericke-Universit at Magdeburg, PF 4120
D-39016 Magdeburg, Germany

Abstract

We consider a general framework for analysing the convergence of multi-grid solvers applied to finite element discretisations of mixed problems, both of conforming and nonconforming type. As a basic new feature, our approach allows to use different finite element discretisations on each level of the multi-grid hierarchy. Thus, in our multi-level approach, accurate higher order finite element discretisations can be combined with fast multi-level solvers based on lower order (nonconforming) finite element discretisations. This leads to the design of efficient multi-level solvers for higher order finite element discretisations.


Contributed June 6, 2001.