Residual-free bubbles for embedded Dirichlet problems

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Robust imposition of Dirichlet boundary conditions on embedded surfaces (2012, methodology): “Logarithmic field We next extend the problem modeling a logarithmic field considered in [32] to a three-dimensional case.”
Extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids (2015, methodology): “In the EFEM with element-wise local enrichments, this boundary condition is in general ignored completely [38–40], whereas in the nodally enriched XFEM it is dealt with either by ad hoc assumptions [17,19] or by complex strategies [45,46].”
Stabilized low-order finite elements for frictional contact with the extended finite element method (2010, methodology): “Existing stabilized methods include Nitsche's method [38], bubble stabilization [17,18,34], and reduced Lagrange methods [2,24,31].”
A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method (2009, methodology): “Efforts were done recently in order to determine automatically this parameter using bubble stabilization (Mourad, Dolbow, and Harari 2007; Dolbow and Franca 2008).”
Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods (2012, methodology): “For this purpose, we vary the interface location with respect to a given structured background mesh in the same spirit as [45].”