A posteriori error estimation for extended finite elements by an extended global recovery

By Marc Duflot, Stéphane P.A. Bordas. 2008

136 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ebe4353552fd102eff72469d70c92e4f483849da

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 Mechanics of Materials

Citations in the corpus

A recovery‐type error estimator for the extended finite element method based on singular+smooth stress field splitting (2008, background): “This was shown by Bordas and Duflot [18,19], who compared extended moving least squares (XMLS) recovery to standard SPR and showed that the latter led to effectivity indices that failed to converge to unity and presented very inadequate recovered solution.”
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].”
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”
The extended/generalized finite element method: An overview of the method and its applications (2010, background): “In Duflot and Bordas [69], the global derivative recovery, as proposed in [135] for the FEM, is extended to enriched finite elements and an associated error indicator is derived.”
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 [10–12, 38].”
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].”
Extended finite element method with global enrichment (2015, methodology): “In standard XFEM those higher order terms can be represented by the FE part of the approximation, in addition since the 13 Page 13 of 81 http://mc.manuscriptcentral.com/nme International Journal for Numerical Methods in Engineering Peer Review O nly tip enrichment functions are weighted by the FE sh”