2007
DOI: 10.1002/nme.2259
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Abstract: SUMMARYThe extended finite element method (XFEM) enables local enrichments of approximation spaces. Standard finite elements are used in the major part of the domain and enriched elements are employed where special solution properties such as discontinuities and singularities shall be captured. In elements that blend the enriched areas with the rest of the domain problems arise in general. These blending elements often require a special treatment in order to avoid a decrease in the overall convergence rate. A … Show more

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Cited by 447 publications
(413 citation statements)
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References 27 publications
(41 reference statements)
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“…Recently an effective and simple approach has been proposed by Fries [45] who used a linearly decreasing weight function for the enrichment in the blending elements. This approach allows one to obtain a conforming approximation and to eliminate partially enriched elements, so that the partition of unity property is everywhere satisfied.…”
Section: Blending Of Enriched and Non-enriched Elementsmentioning
confidence: 99%
“…Recently an effective and simple approach has been proposed by Fries [45] who used a linearly decreasing weight function for the enrichment in the blending elements. This approach allows one to obtain a conforming approximation and to eliminate partially enriched elements, so that the partition of unity property is everywhere satisfied.…”
Section: Blending Of Enriched and Non-enriched Elementsmentioning
confidence: 99%
“…This is particularly important for the crack tip singularity because the convergence of the solution with the mesh size could be rather slow otherwise C··..I hlf2 for the stresses). A useful alternative, which we have tested, is to include the crack tip singularities as enrichment shape functions, as in [34,35,27], Such an approach can recover an optimal order of convergence (1"' ..1 h for stresses) and enables the use of less refined meshes near the cracktip. Of course, it does not help with steep pressure gradients when L 1"' ..1 a.…”
Section: Spatial Discretizationmentioning
confidence: 99%
“…To overcome this deficiency, the nodes outside the radius of the blending elements are also enriched with the near tip solution, see Fig. 1 and the corrected X-FEM approach proposed in [4]. The four enrichment functions F k with k = 1, .…”
Section: Extended Finite Element Methodsmentioning
confidence: 99%