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A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method
Author(s) -
Béchet Éric,
Moës Nicolas,
Wohlmuth Barbara
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2515
Subject(s) - lagrange multiplier , counterexample , mathematics , constraint algorithm , finite element method , space (punctuation) , multiplier (economics) , mathematical analysis , context (archaeology) , mathematical optimization , computer science , discrete mathematics , physics , paleontology , macroeconomics , biology , economics , thermodynamics , operating system
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 © 2008 John Wiley & Sons, Ltd.