Reference : A stable Lagrange multiplier space for stiff interface conditions within the extended fi...
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A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method
Béchet, Eric mailto [Université de Liège - ULg > Département d'aérospatiale et mécanique > Conception géométrique assistée par ordinateur >]
Moes, Nicolas [>Gem, Ecole Centrale de Nantes, Institut GEM, UMR CNRS 6183 1, rue de la No¨e, 44321 Nantes, France > > > > > >]
Wohlmuth, Barbara [>Institute of Applied Analysis and Numerical Simulations (IANS), Universit¨at Stuttgart, Pfaffenwaldring 57, 70529 Stuttgart, Germany > > > > > >]
International Journal for Numerical Methods in Engineering
John Wiley & Sons, Inc
Yes (verified by ORBi)
United Kingdom
[en] extended finite element method ; stiff boundary condition ; Lagrange multiplier space
[en] This paper introduces a new algorithm to define a stable Lagrange multiplier space to impose stiff interface conditions within the context of the extended finite element method. In contrast to earlier approaches. we do not work with an interior penalty formulation as, e.g. for Nitsche techniques, but impose the constraints weakly in terms of Lagrange multipliers. Roughly speaking a stable and optimal discrete Lagrange multiplier space has to satisfy two criteria: a best approximation property and a uniform inf-sup condition. Owing to the fact that the interface does not match the edges of the mesh, the choice of a good discrete Lagrange Multiplier space is not trivial. Here we propose a new algorithm for the local construction of the Lagrange Multiplier space and show that a uniform inf-sup condition is satisfied. A counterexample is also presented, i.e. the inf-sup constant depends on the mesh-size and degenerates as it tends to zero. Numerical results in two-dimensional confirm the theoretical ones. Copyright (C) 2008 John Wiley & Sons, Ltd.
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