Preprint No.
A-99-18
Barbara Wohlmuth, Rolf Krause
Multigrid Methods Based on the Unconstrained Product Space Arising from Mortar Finite Element Discretizations
Abstract: The mortar finite element method allows the coupling of different
discretizations across subregion boundaries. In the original mortar
approach, the Lagrange multiplier space enforcing a weak continuity
condition at the interfaces is defined as a modified finite element
trace space.
Here, we present a new approach, where
the Lagrange multiplier space is replaced by a dual space without
loosing
the optimality of the a priori bounds.
Using the biorthogonality between the nodal basis functions of
this Lagrange
multiplier space and a finite element trace space,
we derive an equivalent symmetric positive definite
variational problem defined on the unconstrained product space.
The introduction of this formulation is based
on a local elimination process for the Lagrange
multiplier. This equivalent approach is the starting point for
the efficient iterative solution by a multigrid method.
To obtain level independent convergence rates for the ${\cal W}$--cycle,
we have to define suitable level dependent bilinear forms.
Keywords: mortar finite elements, Lagrange multiplier, dual space, non--matching triangulations, multigrid methods, level dependent bilinear forms
Mathematics Subject Classification (MSC91): 65N15 Error bounds
, 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Language: ENG
Available: Pr-A-99-18.ps
Contact: Krause, Rolf, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (krause@math.fu-berlin.de)
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