Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods

By R. Gracie, Hongwu Wang, Ted Belytschko. 2008

145 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/18af2beef20e3b0fc34a4febc875971f16369aa7

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 Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

The extended finite element method for fracture in composite materials (2009, methodology): “XFEM that improves the approximation in blending elements described in [23, 24].”
On methods for stabilizing constraints over enriched interfaces in elasticity (2009, methodology): “[9] have recently studied the application of Nitsche’s method to internal boundaries modeled through a mixed X-FEM and discontinuous Galerkin method.”
Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth (2017, background): “This flexibility simplifies local adaptive processes, as the regenerated mesh need not conform to the crack faces [19–21] does not come for free, as (1) numerical integration requires special attention [22–24]; (2) optimal convergence requires enriching a volume independent of the mesh size, thereby”
Extended finite element method with global enrichment (2015, methodology): “Subsequently, displacements are matched by imposing the condition 1 : 1 Note that this procedure also removes completely blending errors [27,28,29,30,31,32].”
Improved conditioning and accuracy of GFEM/XFEM for three-dimensional fracture mechanics (2015, background): “This leads to finite elements which are only partially enriched – the so-called blending elements [12, 13, 19, 22, 27, 46, 50, 52].”
A hybridizable discontinuous Galerkin method for linear elasticity (2009, methodology): “Let us also mention use of DG ‘technology’ for the computation of a locally conservative stress for the continuous Galerkin (CG) method for linear elasticity in [20], and the recent combination of XFEM and DG methods for the approximations of cracks in [21].”
An extended finite element method for fluid flow in partially saturated porous media with weak discontinuities; the convergence analysis of local enrichment strategies (2013, methodology): “This issue has already been addressed in applications to weak discontinuities and a number of techniques have been developed to overcome the drawback caused by the blending elements [30–36].”
A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics (2013, background): “This leads to elements in a finite element mesh that are only partially enriched – the so-called blending elements [12, 13, 20, 22, 24, 34, 40, 41].”
Enhanced blending elements for XFEM applied to linear elastic fracture mechanics (2009, methodology): “[29] develop a discontinuous Galerkin formulation without blending elements in which the continuity is enforced with an internal penalty method.”
The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “[90], the coupling is realized by a discontinuous Galerkin method based on interior penalty terms.”
A review of extended/generalized finite element methods for material modeling (2009, methodology): “Following this viewpoint, Gracie et al [51] introduced a patch-based version of the discontinuous Galerkin formulation, which enforces continuity between the enriched and unenriched patches by an interior penalty method.”