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  "body": "\n## Summary\n\nThe extended finite element method, or XFEM, enriches a standard [[finite element|98GZ9DVHTA]] space with extra functions.\nThese carry known features of the solution, such as a jump across a crack.\nThe enrichment is built with the [[partition of unity|NH739XXVXK]] formed by the usual shape functions.\nSo cracks, interfaces and inclusions can cut through elements, and the mesh does not need to follow them.\nIt was developed in fracture mechanics by Ted Belytschko and coworkers, and is often combined with the [[level-set method|7KWR08FJET]] to describe the moving crack.\nSee the [[definition|35KXRGMAHT]].\n\n## Explanations\n\n### L1 human\n\nA crack in a plate makes the displacement jump across the crack faces.\nOrdinary finite elements are continuous, so they need a mesh that is cut exactly along the crack, and a new mesh whenever the crack grows.\nXFEM keeps a fixed mesh and adds a jump function, such as a step that is $0$ on one side and $1$ on the other, near the crack.\nThe method then finds how much of this step each node needs.\n",
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