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2001-11

NON-NESTED MULTI-LEVEL SOLVERS FOR FINITE ELEMENT DISCRETISATIONS OF MIXED PROBLEMS

by John, V., Knobloch, P., Matthies, G., Tobiska, L..


Series: 2001-11, Preprints

MSC:
65N55 Multigrid methods; domain decomposition
65N30 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods
76D07 Stokes and related (Oseen, etc.) flows

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.

Keywords:
Multi-level method, finite element discretisation, mixed problems, Stokes problem