A corrected XFEM approximation without problems in blending elements

By Thomas-Peter Fries. 2008

566 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/d363a571ade4965a80079650f4385cb568db9632

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Coupling schemes for modeling hydraulic fracture propagation using the XFEM (2013, methodology): “Weak formulation Following [33] the domain V is discretized into a finite element mesh comprising a set of non-overlapping quadrilateral elements.”
The extended finite element method for fracture in composite materials (2009, methodology): “XFEM that improves the approximation in blending elements described in [23, 24].”
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): “In the corrected XFEM formulation, proposed by Fries [33], some modifications are introduced to the standard XFEM formulation as uh (x, t) = ∑”
A coupled SPH-DEM model for fluid-structure interaction problems with free-surface flow and structural failure (2016, unknown): “The FEM as a traditional mesh-based method and its extended versions play an important role in dealing with solid fracture or structural failure problems [32, 33].”
A robust preconditioning technique for the extended finite element method (2011, background): “However not all of them should be used in order to avoid linear dependence [11].”
Strain smoothing in FEM and XFEM (2010, background): “9 The reader will note the very recent papers by Belytschko’s group [44,97] and Fries [39], which provide an improved enrichment scheme to avoid blending errors reported in the literature (e.”
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].”
Higher‐order XFEM for curved strong and weak discontinuities (2009, methodology): “In this study, we will investigate the modified abs-enrichment [38], the corrected XFEM [32], and the standard XFEM with N i (x) of different order than Ni as suggested, e.”