[1] T. Preusser, M. Rumpf, and L. O. Schwen. Finite element simulation of bone microstructures. In 14th Workshop on the Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields, pages 52-66. University of Ulm, 2007.
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The geometric construction of finite element spaces suitable for complicated shapes or microstructured materials is discussed. As an application, the efficient computation of linearized elasticity is considered on them. Geometries are supposed to be implicitly described via 3D voxel data (e. g. μCT scans) associated with a cubic grid. We place degrees of freedom only at the grid nodes and incorporate the complexity of the domain in the hierarchy of finite element basis functions, i.e. constructed by cut off operations at the reconstructed domain boundary. Thus, our method inherits the nestedness of uniform hexahedral grids while still being able to resolve complicated structures. In particular, the canonical coarse scales on hexahedral grid hierarchies can be used in multigrid methods.