2009
DOI: 10.1002/nme.2768
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Abstract: The extended finite element method (XFEM) enables the accurate approximation of solutions with jumps or kinks within elements. Optimal convergence rates have frequently been achieved for linear elements and piecewise planar interfaces. Higher-order convergence for arbitrary curved interfaces relies on two major issues: (i) an accurate quadrature of the Galerkin weak form for the cut elements and (ii) a careful formulation of the enrichment, which should preclude any problems in the blending elements. For (i), … Show more

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Cited by 102 publications
(163 citation statements)
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References 44 publications
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“…A higherorder X-FEM technique (see e.g. [26]) may show some improvement related to these concerns, but we found the approach based on the DG FEM as presented by [1] more natural to extend for our specific demands.…”
Section: Extended Finite Element Methods (X-fem)mentioning
confidence: 94%
“…A higherorder X-FEM technique (see e.g. [26]) may show some improvement related to these concerns, but we found the approach based on the DG FEM as presented by [1] more natural to extend for our specific demands.…”
Section: Extended Finite Element Methods (X-fem)mentioning
confidence: 94%
“…Investigations in the field of XFEM show that it is beneficial to subdivide elements that are cut by the interface into a set of curved geometric entities. In [22], the cut elements are approximated by a set of Lagrangian elements with curved sides. The problem has also been addressed in [24], where an algorithmic approach to decompose cut elements into a set of curved triangles was presented.…”
Section: Figurementioning
confidence: 99%
“…Another technique to resolve the discontinuous integrand is to decompose the cut cells into Lagrangian elements in such a way that the edges of the resulting subcells align with the interface [22]. The use of triangular NURBS-Enhanced Finite Elements [23] in different XFEM settings has also been investigated in [24], based on an approach that is extended in this contribution.…”
mentioning
confidence: 99%
“…This introduces further approximations, although the associated error is deemed small for sufficiently refined meshes, as the ones used in this analysis. It is possible to improve the crack description using higher order elements [23], but this issue has not been considered in this work. …”
Section: Reference Problemmentioning
confidence: 99%