The generalized finite element method

By Theofanis Strouboulis, K. Copps, Ivo Babuska. 2001

671 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/1fb9e06e3b051d59eed61daa39e5cb661aa2e7b8

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Arbitrarily smooth generalized finite element approximations (2006, methodology): “The proposed technique is an instance of the partition of unity method like the hp-cloud [21] [22] and generalized finite element methods [17] [18] [67] [69].”
A two-scale approach for the analysis of propagating three-dimensional fractures (2012, methodology): “The generalized FEM [2] [3] [17] [40] [54] is an instance of the so-called partition of unity method (PUM), which has its origins in the works of Babuška et al. [4] [3] [34] and Duarte and Oden [14] [15] [16] [12] [40].”
The MITC3 shell finite element enriched by interpolation covers (2014, background): “Enriching the finite element procedure is in principle, and theoretically, straightforward but difficulties are encountered in obtaining effective schemes [6–10,29–33].”
Extended finite element method in computational fracture mechanics: a retrospective examination (2015, neutral): “Another instance of the PUFEM is the generalized ﬁnite element method (GFEM), in which hand-book solutions and eigenfunctions for corner singularities and crack problems in elasticity are selected as enrichment functions (Duarte et al. 2000; Strouboulis et al. 2001).”
The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “Numerical handbook functions are also discussed in [172].”
Analysis of three‐dimensional fracture mechanics problems: A two‐scale approach using coarse‐generalized FEM meshes (2010, methodology): “The Generalized or Extended FEM (G/XFEM) [3, 4, 8, 19, 50, 52, 63 , 66] has been successfully applied to the simulation of boundary layers [16], propagating fractures [20, 35, 51, 67], acoustic problems [6, 48], polycrystalline microstructures [ 1, 62], etc.”
Ductile Fracture by Void Growth to Coalescence (2010, methodology): “, (Moes et al., 1999; Strouboulis et al., 2001; Huespe et al., 2009).”
GENERALIZED FINITE ELEMENT METHODS — MAIN IDEAS, RESULTS AND PERSPECTIVE (2004, methodology): “In the problems considered in [37, 38 ], the diagonal elements of A were always dominant and a low tolerance requirement in the adaptive quadrature for evaluating diagonal elements ensured the accuracy of evaluation of o-diagonal elements.”
High‐order extended finite element method for cracked domains (2005, methodology): “Following these ideas, numerical works have been carried out [8–10].”
A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics (2013, background): “Introduction The Generalized or Extended FEM (GFEM/XFEM) [4, 5, 7, 17, 26, 28, 36, 38] has been intensively developed in the last fifteen years and today is available in mainstream commercial Finite Element”