The design and analysis of the Generalized Finite Element Method

By Theofanis Strouboulis, Ivo Babuska, K. Copps. 2000

974 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/e7dd7edc1520c58dc7b723b2194488273c215bbf

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

A review of extended/generalized finite element methods for material modeling (2009, background): “• Higher order Gauss quadrature, which has been demonstrated to perform quite poorly [95]; • Adaptive quadrature for singular functions [95]; • Subdomain quadrature, in which the element is subdivided into quadrature subdomains with boundaries aligned with the discontinuity (e.”
Extended finite element method for three-dimensional crack modelling (2000, methodology): “Strouboulis et al. [ 21 ] used local enrichment functions within the partition of unity framework for modelling re-entrant corners in two dimensions, and in Reference [22], enrichment functions for holes are proposed.”
A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics (2013, methodology): “Further details are provided in [17, 35].”
Extended virtual element method for the Laplace problem with singularities and discontinuities (2019, methodology): “[31], we choose the Neumann boundary data gN”
Derivative recovery and a posteriori error estimate for extended finite elements (2007, methodology): “Other partition of unity enriched finite element methods are the generalized finite element method (GFEM) [37, 38] and Nitsche’s method [22], although the latter’s kinematics is identical to that of the XFEM [5].”
Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method (2010, methodology): “[49] as well as Xiao and Karihaloo [50] use DECUHR [51], an adaptive integration scheme based on nonuniform subdivision of elements for integration of singular functions.”
The 3D Numerical Simulation for the Propagation Process of Multiple Pre-existing Flaws in Rock-Like Materials Subjected to Biaxial Compressive Loads (2016, methodology): “The extended finite element method (XFEM) (Paluszny and Matthai 2009), the generalized finite element method (GFEM) (Strouboulis et al. 2000a, b) and the particle finite element method (PFEM) (Aubry et al. 2005; Pin et al. 2007) are three very commonly used methods that were developed from the FEM,…”