2017 **Abstract:** An accurate implicit description of geometries is enabled by the level-set method.Level-set data is given at the nodes of a higher-order background mesh and the interpolated zero-level sets imply boundaries of the domain or interfaces within. The higher-order accurate integration of elements cut by the zero-level sets is described.The proposed strategy relies on an automatic meshing of the cut elements. Firstly, the zero-level sets are identified and meshed by higher-order interface elements. Secondly, the cut…

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“…Clearly, ${\mathrm{normal\Gamma}}_{q}^{h}$ is defined parametrically through the map even if the original Γ was implicitly given, eg, by the zero isosurface of a level‐set function. See other works for the automatic generation of higher‐order meshes on zero isosurfaces. The discrete unit normal vector is $${\mathit{n}}_{\mathrm{\Gamma}}^{h}=\frac{{\partial}_{r}\mathit{x}\times {\partial}_{s}\mathit{x}}{\Vert {\partial}_{r}\mathit{x}\times {\partial}_{s}\mathit{x}\Vert}$$ and is not smooth across element edges due to the C 0 ‐continuity of the surface mesh.…”

confidence: 99%

“…Clearly, ${\mathrm{normal\Gamma}}_{q}^{h}$ is defined parametrically through the map even if the original Γ was implicitly given, eg, by the zero isosurface of a level‐set function. See other works for the automatic generation of higher‐order meshes on zero isosurfaces. The discrete unit normal vector is $${\mathit{n}}_{\mathrm{\Gamma}}^{h}=\frac{{\partial}_{r}\mathit{x}\times {\partial}_{s}\mathit{x}}{\Vert {\partial}_{r}\mathit{x}\times {\partial}_{s}\mathit{x}\Vert}$$ and is not smooth across element edges due to the C 0 ‐continuity of the surface mesh.…”

confidence: 99%

“…Clearly, Γ h q is defined parametrically through the map (26) even if the original Γ was implicitly given, eg, by the zero isosurface of a level-set function. See other works [39][40][41] for the automatic generation of higher-order meshes on zero isosurfaces. The discrete unit normal vector is…”

confidence: 99%

“…Yet, it cannot be used in general to generate an analysis‐suitable FEM mesh, as it does not need to satisfy requirements on shape and regularity at cell edges and faces, eg, at the transition to the neighboring cells. This approach shares some similarities with the method presented by Fries et al The integration meshes for both considered approaches are displayed in Figure .…”

confidence: 83%

“…Using higher‐order polynomials for the blending, isoparametric transformations are obtained. Blending techniques in the context of extended finite element methods are for instance investigated in previous works …”

confidence: 99%