A bubble‐stabilized finite element method for Dirichlet constraints on embedded interfaces

By Hashem M. Mourad, John Dolbow, I. Harari. 2007

119 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/4f0b41690a5a9d4e935af9a55d1bd386cbb8964f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

A symmetric method for weakly imposing Dirichlet boundary conditions in embedded finite element meshes (2012, background): “However, the finite-element subspaces for the bulk and Lagrange multiplier fields must satisfy the classical inf-sup condition proposed by Babuška [29], which usually leads to the need for stabilization (see [18, 3, 20]).”
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].”
A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method (2009, methodology): “As pointed out in (Mourad, Dolbow, and Harari 2007), these oscillations were also noticed by (Simone 2004) in the context of stiff cohesive law imposed on the faces of a crack.”
A contact algorithm for frictional crack propagation with the extended finite element method (2008, methodology): “The above procedure is essentially equivalent to the domain integral technique described in [ 49 ].”
On methods for stabilizing constraints over enriched interfaces in elasticity (2009, methodology): “Similar work has been done for the Laplace equation with one-sided Dirichlet constraints [18].”
A discontinuous‐Galerkin‐based immersed boundary method (2008, methodology): “This approach was further elaborated by Stenberg[65] and Mourad et al[49].”
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].”