A simple error estimator for extended finite elements

By Stéphane P.A. Bordas, Marc Duflot, P. Le. 2007

106 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/fd7330a5134fa082552a9068a360037c49fcf6ac

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In Computational Mechanics

In Mechanics of Materials

In Ocean Engineering

Citations in the corpus

An extended finite element method for hydraulic fracture problems (2009, methodology): “In this paper, we investigate the use of the extended finite element method (X-FEM) [7–11] for the solution of hydraulic fracture problems in order to avoid re-meshing.”
A posteriori error estimation for extended finite elements by an extended global recovery (2008, methodology): “The principle presented in References [37, 38] is to construct an enhanced stress field interpolated with the same ansatz functions as the displacements, and such that the L2 norm over the whole domain of the difference between the enhanced and original finite element strains (stresses) is minimized”
Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling (2011, methodology): “Much of the well-developed convergence and error estimation theory developed for the finite element method (FEM) can be applied to the XFEM, which is not the case at present for most meshless methods [14].”
A recovery‐type error estimator for the extended finite element method based on singular+smooth stress field splitting (2008, methodology): “[18] and Bordas and Duflot [19] have presented a recovery-based error estimator for XFEM.”
Adaptive analysis using the node‐based smoothed finite element method (NS‐FEM) (2011, methodology): “Recently, an e-type refinement (enrichment adaptivity) that uses an extended global derivative recovery for enriched FEMs such as extended finite element method (XFEM) is also proposed [14–17].”
A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies (2012, methodology): “A simple derivative recovery technique and its associated a posteriori error estimator have been proposed in [10, 11, 12, 38].”
Accurate recovery-based upper error bounds for the extended finite element framework (2010, methodology): “Bordas and co-workers [33–35] have recently developed recovery techniques adapted to the XFEM framework yielding very accurate estimations of the error in energy norm but lacking from the equilibrium constraints needed to guarantee the upper bound property.”
Strain smoothing in FEM and XFEM (2010, unknown): “This is also the subject of recent work on derivative recovery [106] and a posteriori error estimation in XFEM [20,16,34].”