Imposing Dirichlet boundary conditions in the eXtended Finite Element Method
By Gaëtan Bricteux, Jean-François Remacle, Marc Duflot. 2011
138 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/d3be97f330e88ba3cf427c7f3aa22d9e9c3d3559
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Citations in the corpus
- On methods for stabilizing constraints over enriched interfaces in elasticity (2009, methodology): “[5] subsequently developed a stable Lagrange multiplier method based on reducing the number of constraints on the interface.”
- Fictitious domain finite element methods using cut elements (2012, methodology): “In [11] the authors propose a Lagrange multiplier method with an inconsistent penalty term and in [2] using inf-sup stable finite element spaces.”
- Stabilized low-order finite elements for frictional contact with the extended finite element method (2010, methodology): “In [2,31], a stabilized Lagrange space is designed to satisfy the Ladyzhenskaya–Babuska–Brezzi (LBB) condition [1,14], the basic idea being to reduce the number of Lagrange multipliers by certain rules.”
- A 3D interface-enriched generalized finite element method for weakly discontinuous problems with complex internal geometries (2012, methodology): “In this case, other approaches such as Lagrange multipliers or penalty method must be employed to enforce the prescribed values of the solution field at enriched nodes [32,33].”
- Robust imposition of Dirichlet boundary conditions on embedded surfaces (2012, methodology): “[6] developed a stable Lagrange multiplier on the basis of a vital vertex algorithm.”
- The extended/generalized finite element method: An overview of the method and its applications (2010, background): “[123], this “convenient” choice leads to oscillations in the multiplier and decreases the overall convergence rate.”
- Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods (2012, methodology): “[13] developed a coarsening strategy for the X-FEM and Kim et al.”