On strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method

By H. Ji, John Dolbow. 2004

198 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/87c9fcfc8379a8f053f2c829c314f1a106f74633

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In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources (2006, background): “where M is the set of all Lagrange multiplier nodes [6].”
On methods for stabilizing constraints over enriched interfaces in elasticity (2009, methodology): “[18] and Ji and Dolbow [7] but nothing has yet been investigated in the context of elasticity problems.”
A review of extended/generalized finite element methods for material modeling (2009, methodology): “The continuity constraint can be imposed either by Lagrange multipliers or by Nitsche’s method [60, 78].”
Robust imposition of Dirichlet boundary conditions on embedded surfaces (2012, methodology): “In principle, both the stable method of Béchet et al. and the stabilized method of Dolbow and Harari readily extend to three-dimensional problems, but no convergence studies have been published to date.”
Stabilized low-order finite elements for frictional contact with the extended finite element method (2010, background): “A challenging aspect of the problem is the enforcement of the contact condition, whether it be in the context of classical nonlinear contact mechanics in which element sides are aligned to the contact faces [26,36,37,39,40,42,49,50], or in the framework of the assumed enhanced strain or extended FEm”
Imposing Dirichlet boundary conditions in the extended finite element method (2006, methodology): “The difficulty of choosing the proper Lagrange multiplier space to enforce interfacial constraints in the X-FEM framework was already observed by Ji and Dolbow [16].”
A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries (2006, unknown): “[30, 31], are equally feasible, we have preferred not to make the variational form depending on a specific method, and therefore we have not incorporated penalty terms in the variational form.”
Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods (2012, methodology): “The most convenient choice of the basis functions for interpolating the Lagrange multipliers violates the Ladyzhenskaya–Babuska– Brezzi (LBB) condition, resulting in an overly constrained system, which manifests as artificial oscillations in the multiplier field [8].”
A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method (2009, methodology): “In (Ji and Dolbow 2004), the authors illustrate through numerical experiments that a naive choice for the Lagrange multiplier space, i.e., a piecewise linear ansatz space on the interface with a degree of freedom at each node obtained by cutting the interface with the edges of the two-dimensional…”
A bubble‐stabilized finite element method for Dirichlet constraints on embedded interfaces (2007, background): “Additional emphasis has been placed on this issue by the recent work of Ji and Dolbow [10] and Moës et al. [11] with regard to the eXtended Finite Element Method (X-FEM).”
A contact algorithm for frictional crack propagation with the extended finite element method (2008, methodology): “The latter class of methods are often called the extended FE methods [22–39].”
Extended finite element method in computational fracture mechanics: a retrospective examination (2015, unknown): “Another question concerns the stability of the formulation as the effective stiffness of the interface increases, an issue ﬁrst raised by Ji and Dolbow (2004).”
A numerical strategy for investigating the kinetic response of stimulus-responsive hydrogels (2005, background): “Similar results were reported by Ji and Dolbow (2004). We next examine the accuracy of the domain-integral approximations (6.”