Imposing Dirichlet boundary conditions in the eXtended Finite Element Method

Bricteux, Gaëtan;Remacle, Jean-François;Duflot, Marc
(2011) Fifth International Conference on Advanced COmputationalMethods in ENgineering — Location: Liège (14.November.2011)

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Abstract
The imposition of Dirichlet boundary conditions in a non conformal mesh can be done with the use of Lagrange multipliers. But this leads to an over-constrained problem that produces an unstable solution if the finite element subspace for the Lagrange multipliers field does not satisfy the inf-sup condition. A stabilization technique is presented, with on a parameter depending on the mesh size. A benchmark is resolved to validate the stability of our method.
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Bricteux, G. (2011). Imposing Dirichlet boundary conditions in the eXtended Finite Element Method. Fifth International Conference on Advanced COmputationalMethods in ENgineering, Liège. https://hdl.handle.net/2078.5/39036